Algorithms


Files

file  accessible.hh
 Algorithms for accessible/coaccessible states computation.
file  aci_canonical.hh
 Declaration for the canonical() algorithm.
file  aut_to_exp.hh
 This file provides converter from automaton to expression.
file  backward_realtime.hh
 Algorithms to make an automaton realtime.
file  berry_sethi.hh
 Contains the declaration for the Berry-Sethi algorithm.
file  brzozowski.hh
 Contains the declaration for the Brzozowski algorithm.
file  complement.hh
 Complementation algorithm for Boolean automata.
file  complete.hh
 Completion algorithm for deterministic and Boolean automaton.
file  composition_cover.hh
 Composition for normalized and sub-normalized transducers seen as automata over a free monoid product.
file  concatenate.hh
 This file provides the general concatenation algorithm.
file  derived_term_automaton.hh
 Provides a converter from expression to automaton based on derivatives.
file  determinize.hh
 Boolean automata determinization.
file  domain.hh
 Domain algorithm.
file  eps_removal.hh
 This files declares the backward and forward eps_removal algorithm.
file  eps_removal_sp.hh
 This files declares the backward and forward eps_removal algorithm.
file  equivalent.hh
 This file contains the declarations for the are_equivalent() algorithm.
file  eval.hh
 This file provides the evaluation of a word w.r.t an automaton.
file  evaluation_fmp.hh
 Evaluation over normalized and sub-normalized transducers seen as automata over a free monoid product.
file  extension.hh
 Declarations for extension().
file  finite_support_conversion.hh
 Conversion between finite support application types.
file  fmp_to_rw.hh
 This file provides a transformation function that computes the Rational Weight transducer of a FMP automaton.
file  forward_realtime.hh
 Algorithms to make an automaton realtime.
file  has_succ_comp.hh
 Declaration of has_succ_comp().
file  image.hh
 Image projection for transducers.
file  initial_derivation.hh
 Declaration of the initial derivation visitor, used for smart_derivative_automaton.
file  evaluation.hh
 Undocumented stuff.
file  outsplitting.hh
 Outsplitting and insplitting algorithms for normalized and sub-normalized fmp_transducers.
file  is_ambiguous.hh
 Test for ambiguity.
file  is_deterministic.hh
 Boolean automata determinization.
file  is_empty.hh
 Declaration of is_empty().
file  is_letterized.hh
 Letter-to-letter feature testing.
file  is_normalized.hh
 Test for transducer normalization.
file  isomorph.hh
 This files contains the declaration for the are_isomorphic() algorithm.
file  krat_exp_cderivation.hh
 Declaration for the cderivate() algorithms.
file  krat_exp_constant_term.hh
 Declaration for the constant_term() algorithm.
file  krat_exp_derivation.hh
 Declaration for the derivate() algorithms.
file  krat_exp_expand.hh
 Expand a k-rational-expression.
file  krat_exp_flatten.hh
 This file holds the declaration of the flatten() algorithm.
file  krat_exp_linearize.hh
 Declarations for the linearize() algorithm.
file  krat_exp_partial_derivation.hh
 Declarations for the partial_derivate() algorithm.
file  krat_exp_realtime.hh
 Declarations of the realtime() algorithm for rational expressions.
file  letter_to_letter_composition.hh
 Undocumented stuff.
file  minimization_hopcroft.hh
 This file provides minimization and quotient algorithms.
file  minimization_moore.hh
 This file containes the declaration of minimization_moore().
file  normalized.hh
 Thompson normalization operations.
file  normalized_composition.hh
 Composition for normalized and sub-normalized transducers seen as automata over a free monoid product.
file  product.hh
 Declarations of product().
file  projection.hh
 Undocumented stuff.
file  realtime.hh
 General algorithms concerning realtime aspect of automata.
file  realtime_decl.hh
 Declaration of the realtime() function.
file  rw_composition.hh
 Composition of two Rational-Weight transducers.
file  rw_to_fmp.hh
 This file provides a transformation function that computes the equivalent FMP automaton of a Rational Weight tranducer.
file  search.hh
 Rational expression search in text.
file  standard.hh
 Several algorithms concerning standard automata.
file  standard_of.hh
 This file provides a converter from expression to standard automaton.
file  sub_automaton.hh
 This file provides the extraction of sub automaton.
file  sub_normalize.hh
 Sub-normalization algorithm for FMP transducers.
file  sum.hh
 Summing of automata.
file  thompson.hh
 The thompson automaton.
file  trim.hh
 Declaration of useful_states() and trim().

Classes

struct  KRatExpFlatten
struct  linearize_element
 The types of a linearized expression. More...
struct  FindBestSearch
 Specific implementation for search(). More...
struct  WindowedBackSearch
 Specific implementation for search(). More...

Determinization algorithms

template<typename A, typename T>
Element< A, T > determinize (const Element< A, T > &a)
 Returns the determinized of a Boolean automaton.
template<typename A, typename T>
Element< A, T > determinize (const Element< A, T > &a, std::map< typename T::hstate_t, std::set< typename T::hstate_t > > &m)
 Returns the determinized of a Boolean automaton.

FMP automaton to rational weight transducer algorithm.

Compute the equivalent Rational Weight transducer of a FMP automaton.

Please note that for the moment this function works only if the support of each transition is finite.

Algorithm : If the FMP contains transitions with "complex" expression (E), i.e. infinite support, then Thompson of E. With the resulting automaton apply a conversion. i.e. (a,x) -> a|x

template<typename S, typename T, typename SS, typename TT>
Element< SS, TT > & fmp_to_rw (const Element< S, T > &fmp, Element< SS, TT > &res)

Product algorithm

Returns a fresh automaton that is the product of the two input ones.

Precondition:
The two input automata must be realtime.


template<typename A, typename T, typename U>
Element< A, T > product (const Element< A, T > &lhs, const Element< A, U > &rhs, const bool use_geometry=false)
template<typename A, typename T, typename U>
Element< A, T > product (const Element< A, T > &lhs, const Element< A, U > &rhs, std::map< typename T::hstate_t, std::pair< typename T::hstate_t, typename U::hstate_t > > &, const bool use_geometry=false)

Rational Weight transducer to FMP automaton conversion

template<typename S, typename T, typename SS, typename TT>
Element< SS, TT > & rw_to_fmp (const Element< S, T > &trans, Element< SS, TT > &res)
 Compute the equivalent FMP automaton of a Rational Weight transducer.

Functions

template<typename A, typename T>
std::set< typename
automaton_traits< T >
::hstate_t > 		accessible_states (const Element< A, T > &a)
 Return accessible states.
template<typename A, typename T>
Element< A, T > accessible (const Element< A, T > &a)
 Extract the sub-automaton composed of accessible states.
template<typename A, typename T>
void accessible_here (Element< A, T > &a)
 In-place extract the sub-automaton of accessible states.
template<typename A, typename T>
std::set< typename
automaton_traits< T >
::hstate_t > 		coaccessible_states (const Element< A, T > &a)
 Return co-accessible states.
template<typename A, typename T>
Element< A, T > coaccessible (const Element< A, T > &a)
 Extract the sub-automaton composed of co-accessible states.
template<typename A, typename T>
void coaccessible_here (Element< A, T > &a)
 In-place extract the sub-automaton of co-accessible states.
template<class Series, class T>
Element< Series, T > canonical (const Element< Series, T > &exp)
 Transform a krat expression into its canonical form, following aci-rules.
template<typename A, typename T>
Element< A, T >::series_set_elt_t aut_to_exp (const Element< A, T > &a)
 Returns a series which describes the language of the automaton.
template<typename A, typename T, typename Chooser_>
Element< A, T >::series_set_elt_t aut_to_exp (const Element< A, T > &a, const Chooser_ &c)
 Returns a series which describes the language of the automaton.
template<typename A, typename T>
void backward_realtime_here (Element< A, T > &a)
 In place modification of the automaton to make it realtime.
template<typename A, typename T>
Element< A, T > backward_realtime (const Element< A, T > &a)
 Returns a fresh realtime automaton.
template<typename A, typename T, typename Exp>
void berry_sethi (Element< A, T > &, const Exp &)
 Build an automaton from an expression using the Berry-Sethi construction.
template<typename A, typename T, typename Exp>
void brzozowski (Element< A, T > &, const Exp &)
 Build an automaton from an expression using the Brzozowski construction.
template<typename A, typename T>
void complement_here (Element< A, T > &a)
 Complement in place the set of final states.
template<typename A, typename T>
Element< A, T > complement (const Element< A, T > &a)
 Complement the set of final states.
template<typename A, typename T>
void complete_here (Element< A, T > &a)
 Make the transition function of an automaton total w.r.t alphabet.
template<typename A, typename T>
Element< A, T > complete (const Element< A, T > &a)
 Make the transition function of an automaton total w.r.t alphabet.
template<class A, class T>
bool is_complete (const Element< A, T > &a)
 Test if the transition function is complete for each state.
template<typename S, typename T>
Element< S, T > composition_cover (const Element< S, T > &fmp)
 Facade for composition cover.
template<typename S, typename T>
Element< S, T > composition_co_cover (const Element< S, T > &fmp)
 Facade for composition co-cover.
template<class A, class T>
Element< A, T > concatenate (const Element< A, T > &lhs, const Element< A, T > &rhs)
 Return the concatenation of two automata.
template<class A, class T>
void concatenate_here (Element< A, T > &lhs, const Element< A, T > &rhs)
 In place concatenation of two automata.
template<typename A, typename T, typename Exp>
void derived_term_automaton (Element< A, T > &a, const Exp &e)
 Convert a krat expression into an automaton using derivatives.
template<typename A, typename T, typename Exp>
Element< A, T > derived_term_automaton (const Exp &e)
 Convert a krat expression into an automaton using derivatives.
template<typename A, typename T, typename Exp>
Element< A, T > broken_derived_term_automaton (const Exp &e)
 Convert a krat expression into an automaton using derivatives.
template<typename A, typename T>
void eps_removal_here (Element< A, T > &a, misc::direction_type dir=misc::backward)
 In place eps_removal of an automaton (default is backward eps_removal).
template<typename A, typename T>
Element< A, T > eps_removal (const Element< A, T > &a, misc::direction_type dir=misc::backward)
 Eps_Removal of an automaton (default is backward eps_removal).
template<typename A, typename T>
void backward_eps_removal_here (Element< A, T > &a)
 In place backward eps_removal of an automaton.
template<typename A, typename T>
Element< A, T > backward_eps_removal (const Element< A, T > &a)
 Backward eps_removal of an automaton.
template<typename A, typename T>
void forward_eps_removal_here (Element< A, T > &a)
 In place forward eps_removal of an automaton.
template<typename A, typename T>
Element< A, T > forward_eps_removal (const Element< A, T > &a)
 Forward eps_removal of an automaton.
template<typename A, typename T>
void eps_removal_here_sp (Element< A, T > &a, misc::direction_type dir=misc::backward)
 In place eps_removal_sp of an automaton (default is backward eps_removal).
template<typename A, typename T>
Element< A, T > eps_removal_sp (const Element< A, T > &a, misc::direction_type dir=misc::backward)
 Eps_Removal of an automaton (default is backward eps_removal).
template<typename A, typename T>
void backward_eps_removal_here_sp (Element< A, T > &a)
 In place backward eps_removal_sp of an automaton.
template<typename A, typename T>
Element< A, T > backward_eps_removal_sp (const Element< A, T > &a)
 Backward eps_removal_sp of an automaton.
template<typename A, typename T>
void forward_eps_removal_here_sp (Element< A, T > &a)
 In place forward eps_removal_sp of an automaton.
template<typename A, typename T>
Element< A, T > forward_eps_removal_sp (const Element< A, T > &a)
 Forward eps_removal_sp of an automaton.
template<typename S, typename A, typename B>
bool are_equivalent (const Element< S, A > &a, const Element< S, B > &b)
 Returns true iff the two boolean automata are equivalents, i.e., if they recognize the same language.
template<typename A, typename T, typename W>
Element< A, T >::semiring_elt_t eval (const Element< A, T > &a, const W &word)
 Return the image of a word by an automaton.
template<typename SA, typename TA, typename ST, typename TT, typename SARET, typename TARET>
void evaluation_fmp (const Element< ST, TT > &, const Element< SA, TA > &, Element< SARET, TARET > &)
 Evaluation over normalized and sub-normalized transducers, seen as automata over a free monoid product.
template<typename S, typename T>
identity_transducer_helper< S,
T >::ret 		extension (const Element< S, T > &)
 Extend an automaton to a transducer.
template<typename SA, typename TA, typename ST, typename TT>
Element< ST, TT > extension (const Element< SA, TA > &, const Element< ST, TT > &)
 Extend an automaton to a transducer.
template<typename S, typename T, typename Ss, typename Ts>
void finite_support_convert (Element< S, T > &dst, const Element< Ss, Ts > &org)
 Finite support conversion.
template<typename A, typename T>
void forward_realtime_here (Element< A, T > &a)
 In place modification of the automaton to make it realtime.
template<typename A, typename T>
Element< A, T > forward_realtime (const Element< A, T > &a)
 Returns a fresh realtime automaton.
template<typename A, typename T>
bool has_succ_comp (const Element< A, T > &a)
 Return true if the automaton has successful computation (has at least one state that is both accessible and co-accessible), false otherwise.
template<typename SA, typename TA, typename ST, typename TT, typename SARET, typename TARET>
void evaluation (const Element< SA, TA > &, const Element< ST, TT > &, Element< SARET, TARET > &)
 Evaluate for a "letterized" automaton and a realtime transducer.
template<typename S, typename A>
bool is_ambiguous (const Element< S, A > &aut)
 Test the ambiguity of automaton.
template<typename A, typename T>
bool is_deterministic (const Element< A, T > &a)
 Test if an automaton is deterministic.
template<typename A, typename T>
bool is_empty (const Element< A, T > &a)
 Return true if the automaton is empty (has no state), false otherwise.
template<typename S, typename A>
bool is_letterized_transducer (const Element< S, A > &t)
 Test the letter to letter features.
template<typename S, typename A>
bool is_normalized_transducer (const Element< S, A > &t)
 Test the normalization of transducer.
template<typename A, typename T>
bool are_isomorphic (const Element< A, T > &a, const Element< A, T > &b)
 Returns true if the two automata are isomorphic.
template<class Series, class T, class Letter>
Element< Series, T > cderivate (const Element< Series, T > &exp, Letter a)
 The c-derivative of the krat expression w.r.t to a letter.
template<class Series, class T, class Word>
Element< Series, T > word_cderivate (const Element< Series, T > &exp, Word a)
 The c-derivative of the krat expression w.r.t to a word.
template<class Series, class T>
std::pair< typename Element
< Series, T >::semiring_elt_t,
bool > 		constant_term (const Element< Series, T > &exp)
 Return the constant term of the krat expression.
template<class Series, class T, class Letter>
std::pair< Element< Series, T >
, bool > 		derivate (const Element< Series, T > &exp, Letter a)
 The antimirov derivative of the krat expression w.r.t to a letter.
template<class Series, class T, class Word>
std::pair< Element< Series, T >
, bool > 		word_derivate (const Element< Series, T > &exp, Word a)
 The antimirov derivative of the krat expression w.r.t to a word.
template<class Series, class T>
std::list< typename
Series::monoid_t::alphabet_t::letter_t > 		flatten (const Element< Series, T > &exp)
 This algorithm extracts the letters from a rational expression.
template<class Series, class T>
linearize_element< Series, T >
::element_t 		linearize (const Element< Series, T > &exp)
 The linearization of the krat expression.
template<class Series, class T, class Letter>
std::pair< std::set< Element
< Series, T > >, bool > 		partial_derivate (const Element< Series, T > &exp, Letter a)
 The partial derivative of the krat expression w.r.t to a letter.
template<class S, class T>
Element< S, T > letter_to_letter_composition (const Element< S, T > &lhs, const Element< S, T > &rhs)
 Undocumented.
template<typename A, typename T>
Element< A, T > minimization_hopcroft (const Element< A, T > &a)
 Return the minimal automaton using the hopcroft algorithm.
template<typename A, typename T>
Element< A, T > quotient (const Element< A, T > &a)
 Return the quotient of a non-deterministic acceptor.
template<typename A, typename T>
Element< A, T > minimization_moore (const Element< A, T > &a)
 Returns the minimal deterministic automaton associated to the input one.
template<typename A, typename T>
Element< A, T > co_minimization_moore (const Element< A, T > &a)
 Returns the co-minimal co-deterministic automaton associated to the input one.
template<typename A, typename T>
void minimization_moore_here (Element< A, T > &a)
 Minimalize the deterministic input automaton.
template<typename A, typename T>
void co_minimization_moore_here (Element< A, T > &a)
 Co-minimalize the co-deterministic input automaton.
template<typename A, typename T>
Element< A, T > normalize (const Element< A, T > &a)
 Return the fresh thompson-normalized automaton.
template<typename A, typename T>
void normalize_here (Element< A, T > &a)
 In-place normalize to the thompson form.
template<typename A, typename T>
bool is_normalized (const Element< A, T > &a)
 Return true if the input automaton is thompson-normalized.
template<typename A, typename T, typename U>
void union_of_normalized_here (Element< A, T > &lhs, const Element< A, U > &rhs)
 Do the in-place union of two thompson-normalized automata.
template<typename A, typename T, typename U>
Element< A, T > union_of_normalized (const Element< A, T > &lhs, const Element< A, U > &rhs)
 Return the fresh union of two thompson-normalized automata.
template<typename A, typename T, typename U>
void concatenate_of_normalized_here (Element< A, T > &lhs, const Element< A, U > &rhs)
 Do the in-place concatenation of two thompson-normalized automata.
template<typename A, typename T, typename U>
Element< A, T > concatenate_of_normalized (const Element< A, T > &lhs, const Element< A, U > &rhs)
 Return the fresh concatenation of two thompson-normalized automata.
template<typename A, typename T>
void star_of_normalized_here (Element< A, T > &a)
 Do in-place star transformation on the thompson-normalized input.
template<typename A, typename T>
Element< A, T > star_of_normalized (const Element< A, T > &a)
 Return the fresh star transformation of its normalized input.
template<typename S, typename T>
void compose (const Element< S, T > &lhs, const Element< S, T > &rhs, Element< S, T > &ret)
 Composition for weighted normalized and sub-normalized transducers, seen as automata over a free monoid product.
template<typename S, typename T>
Element< S, T > compose (const Element< S, T > &lhs, const Element< S, T > &rhs)
 Composition for weighted normalized and sub-normalized transducers, seen as automata over a free monoid product.
template<typename S, typename T>
void u_compose (const Element< S, T > &lhs, const Element< S, T > &rhs, Element< S, T > &ret)
 Unambiguous composition for weighted normalized and sub-normalized transducers, seen as automata over a free monoid product.
template<typename S, typename T>
Element< S, T > u_compose (const Element< S, T > &lhs, const Element< S, T > &rhs)
 Unambiguous composition for weighted normalized and sub-normalized transducers, seen as automata over a free monoid product.
template<typename auto_t, typename trans_t>
void set_states (const trans_t &, auto_t &, std::map< typename trans_t::hstate_t, typename auto_t::hstate_t > &)
template<typename A, typename T>
void realtime_here (Element< A, T > &a, misc::direction_type type)
 In place modification of the automaton to make it realtime.
template<typename A, typename T>
Element< A, T > realtime (const Element< A, T > &a, misc::direction_type type)
 Returns a fresh realtime automaton.
template<typename S, typename T>
Element< S, T > realtime (const Element< S, T > &e)
 Calls the do_realtime function for rational expression or automata.
template<typename S, typename T>
void realtime_here (Element< S, T > &e)
 Calls the do_realtime_here function for rational expression or automata.
template<typename S, typename T>
bool is_realtime (const Element< S, T > &e)
 Test whether an automaton or a regular expression is realtime.
template<typename S, typename T>
void rw_composition (const Element< S, T > &, const Element< S, T > &, Element< S, T > &)
 Composition for Rational-Weight transducers.
template<typename S, typename T>
Element< S, T > rw_composition (const Element< S, T > &, const Element< S, T > &)
 Composition for Rational-Weight transducers.
template<class InputIterator, class FoundFunctor, class Series, class T>
void search (const Element< Automata< Series >, T > &a, const InputIterator &begin, const InputIterator &end, typename Element< Automata< Series >, T >::letter_t eol, FoundFunctor &f)
 Search for a rational expression into a text.
template<class Series, class T, class StatesSet>
static unsigned int compute_distances (const Element< Automata< Series >, T > &a, std::vector< StatesSet > &distances)
 Compute distances from initial states to final states.
template<class InputIterator, class Series, class T, class StatesSet>
static std::pair< bool,
unsigned int > 		window_backsearch (const misc::Window< InputIterator, typename Element< Automata< Series >, T >::letter_t > &w, const Element< Automata< Series >, T > &a, const std::vector< StatesSet > &distances)
 Back search inside a window.
template<class InputIterator, class FoundFunctor, class Series, class T>
static InputIterator confirm_and_report_match (const misc::Window< InputIterator, typename Element< Automata< Series >, T >::letter_t > &w, const Element< Automata< Series >, T > &a, FoundFunctor &f)
 Finds the longest match of a starting from w, and report it to the functor.
template<typename A, typename T>
void standardize (Element< A, T > &a)
 Returns a standard automaton associated to the input.
template<typename A, typename T>
bool is_standard (const Element< A, T > &a)
 Returns true if the input automaton is standard.
template<typename A, typename T, typename U>
void union_of_standard_here (Element< A, T > &lhs, const Element< A, U > &rhs)
 In-place union of two standard automata.
template<typename A, typename T, typename U>
Element< A, T > union_of_standard (const Element< A, T > &lhs, const Element< A, U > &rhs)
 Return a fresh union of two standard automata.
template<typename A, typename T, typename U>
void concat_of_standard_here (Element< A, T > &lhs, const Element< A, U > &rhs)
 In-place concatenation of two standard automata.
template<typename A, typename T, typename U>
Element< A, T > concat_of_standard (const Element< A, T > &lhs, const Element< A, U > &rhs)
 Return a fresh concatenation of two standard automata.
template<typename A, typename T>
void star_of_standard_here (Element< A, T > &a)
 In-place star transformation of a standard automata.
template<typename A, typename T>
Element< A, T > star_of_standard (const Element< A, T > &a)
 Return the fresh star transformation of a standard automata.
template<typename A, typename T, typename Exp>
void standard_of (Element< A, T > &a, const Exp &e)
 Convert a rational expression into a standard automaton.
template<typename A, typename T, typename StatesSet>
Element< A, T > sub_automaton (const Element< A, T > &a, const StatesSet &s, bool check_states=true)
 Returns a fresh automaton that is the sub-automaton defined by a set.
template<typename A, typename T, typename StatesSet>
void sub_automaton_here (Element< A, T > &a, const StatesSet &s, bool check_states=true)
 Select a sub-automaton into a given automaton.
template<class S, class T>
Element< S, T > sub_normalize (const Element< S, T > &a)
 Sub-normalize a FMP transducer.
template<class S, class T1, class T2>
void sub_normalize (const Element< S, T1 > &a, Element< S, T2 > &res)
 Sub-normalize a FMP transducer.
template<class S, class T>
void sub_normalize_here (Element< S, T > &a)
 Sub-normalize a FMP transducer, in place version.
template<class S, class T>
bool is_sub_normalized (const Element< S, T > &a)
 Check if a FMP transducer is sub-normalized.
template<typename A, typename T, typename U>
void sum_here (Element< A, T > &lhs, const Element< A, U > &rhs)
 In place summing of two automata.
template<typename A, typename T, typename U>
Element< A, T > sum (const Element< A, T > &lhs, const Element< A, U > &rhs)
 Summing of two automata.
template<typename A, typename T, typename Letter, typename Weight>
void thompson_of (Element< A, T > &out, const rat::exp< Letter, Weight > &kexp)
 The Thompson automaton associated to the krat expression.
template<class AutoType, class S, class T>
Element< Automata< S >, AutoType > thompson_of (const Element< S, T > &exp)
 The Thompson automaton associated to the krat expression.
template<typename lhs_t, typename rhs_t>
void transpose (lhs_t &dst, const rhs_t &from)
 Transposition of an automaton.
template<typename auto_t>
auto_t transpose (const auto_t &from)
 Return a fresh transposed automaton.
template<typename A, typename T>
std::set< typename T::hstate_t > useful_states (const Element< A, T > &a)
 Returns a useful states of the automaton (start reachable and final co-).
template<typename A, typename T>
Element< A, T > trim (const Element< A, T > &a)
 Return a fresh automaton in which non useful states are removed.
template<typename A, typename T>
void trim_here (Element< A, T > &a)
 Trim a.

Function Documentation

std::set< typename automaton_traits< T >::hstate_t > accessible_states ( const Element< A, T > &  a  )  [inline]

Return accessible states.

This functions returns the accessible states set of its input automaton.

Parameters:
a The input automaton.
See also:
accessible(), coaccessible(), coaccessible_states()

Definition at line 81 of file accessible.hxx.

References Element::structure().

Referenced by vcsn::accessible(), and vcsn::accessible_here().

Element< A, T > accessible ( const Element< A, T > &  a  )  [inline]

Extract the sub-automaton composed of accessible states.

This function returns a fresh sub-automaton of its input containing only accessible states.

Parameters:
a The input automaton.
See also:
accessible_here(), accessible_states(), coaccessible(), coaccessible_states()

Definition at line 96 of file accessible.hxx.

References vcsn::accessible_states(), and vcsn::sub_automaton().

void accessible_here ( Element< A, T > &  a  )  [inline]

In-place extract the sub-automaton of accessible states.

This function computes the sub-autmaton of accessible states from its input automaton. The operation is performed in-place.

Parameters:
a An in/out parameter which contains the automaton to work on as input and the result as output.
See also:
accessible(), accessible_states(), coaccessible(), coaccessible_states()

Definition at line 89 of file accessible.hxx.

References vcsn::accessible_states(), and vcsn::sub_automaton_here().

std::set< typename automaton_traits< T >::hstate_t > coaccessible_states ( const Element< A, T > &  a  )  [inline]

Return co-accessible states.

This functions returns the co-accessible states set of its input automaton, i.e. states which are accessible from final states.

Parameters:
a The input automaton.
See also:
coaccessible(), accessible(), accessible_states()

Definition at line 115 of file accessible.hxx.

References Element::structure().

Referenced by vcsn::coaccessible(), and vcsn::coaccessible_here().

Element< A, T > coaccessible ( const Element< A, T > &  a  )  [inline]

Extract the sub-automaton composed of co-accessible states.

This function returns a fresh sub-automaton of its input containing only co-accessible states, i.e. states which are accessible from final states.

Parameters:
a The input automaton.
See also:
coaccessible_here(), coaccessible_states(), accessible(), accessible_states()

Definition at line 122 of file accessible.hxx.

References vcsn::coaccessible_states(), and vcsn::sub_automaton().

void coaccessible_here ( Element< A, T > &  a  )  [inline]

In-place extract the sub-automaton of co-accessible states.

This function computes the sub-autmaton of co-accessible states from its input automaton. The operation is performed in-place.

Parameters:
a An in/out parameter which contains the automaton to work on as input and the result as output.
See also:
coaccessible(), coaccessible_states(), accessible(), accessible_states()

Definition at line 129 of file accessible.hxx.

References vcsn::coaccessible_states(), and vcsn::sub_automaton_here().

Element< A, T >::series_set_elt_t aut_to_exp ( const Element< A, T > &  a  )  [inline]

Returns a series which describes the language of the automaton.

This algorithm works on every kind of series. However, if, during the computation, it must take the star of it, it can fail. By passing a "generalized" automaton, that is an automaton with rational expression as label, you will be sure to have the algorithm succeed since we can always take the star of a rational expression.

Parameters:
a The automaton to convert.
Returns:
A rational series that describes the language of the automaton.
See also:
generalized()

Definition at line 364 of file aut_to_exp.hxx.

Element< A, T >::series_set_elt_t aut_to_exp ( const Element< A, T > &  a,
const Chooser_ &  c 
) [inline]

Returns a series which describes the language of the automaton.

This algorithm works on every kind of series. However, if, during the computation, it must take the star of it, it can fail. By passing a "generalized" automaton, that is an automaton with rational expression as label, you will be sure to have the algorithm succeed since we can always take the star of a rational expression.

Parameters:
a The automaton to work on.
c An object-function that returns the next state to remove from the current state and the automaton.
Returns:
A rational series that describes the language of the automaton.
See also:
generalized()

Definition at line 355 of file aut_to_exp.hxx.

References Element::structure().

void backward_realtime_here ( Element< A, T > &  a  )  [inline]

In place modification of the automaton to make it realtime.

Make an automaton realtime, using backward version of eps_removal for building.

Parameters:
a The automaton to make realtime.
See also:
realtime(), backward_realtime(), forward_realtime_here()

Definition at line 39 of file backward_realtime.hxx.

References Element::structure().

Element< A, T > backward_realtime ( const Element< A, T > &  a  )  [inline]

Returns a fresh realtime automaton.

Build a fresh realtime automaton from those given, using backward version of eps_removal.

Parameters:
a The automaton to make realtime.
See also:
realtime(), backward_realtime_here(), forward_realtime()

Definition at line 57 of file backward_realtime.hxx.

References Element::structure().

void complement_here ( Element< A, T > &  a  )  [inline]

Complement in place the set of final states.

Parameters:
a The deterministic Boolean automaton to complement.
Precondition:
The input automaton must be complete and deterministic.
See also:
complement()
Author:
Yann Régis-Gianas

Definition at line 38 of file complement.hxx.

References vcsn::is_complete(), and vcsn::is_deterministic().

Referenced by vcsn::complement().

Element< A, T > complement ( const Element< A, T > &  a  )  [inline]

Complement the set of final states.

Parameters:
a the deterministic Boolean automaton to complement.
Precondition:
the input automaton must be complete and deterministic.
See also:
complement_here()
Author:
Yann Régis-Gianas

Definition at line 59 of file complement.hxx.

References vcsn::complement_here().

void complete_here ( Element< A, T > &  a  )  [inline]

Make the transition function of an automaton total w.r.t alphabet.

Note:
This algorithm works in place.
Parameters:
a the deterministic and Boolean automaton to complete.
Precondition:
a must be a realtime automaton
See also:
complete(), is_complete()
Author:
Yann Régis-Gianas

Definition at line 37 of file complete.hxx.

References vcsn::is_realtime(), and Element::structure().

Referenced by vcsn::complete().

Element< A, T > complete ( const Element< A, T > &  a  )  [inline]

Make the transition function of an automaton total w.r.t alphabet.

Note:
This algorithm returns a fresh automaton.
Parameters:
a the deterministic and Boolean automaton to complete.
Precondition:
a must be a realtime automaton
See also:
complete_here(), is_complete()
Author:
Yann Régis-Gianas

Definition at line 82 of file complete.hxx.

References vcsn::complete_here().

bool is_complete ( const Element< A, T > &  a  )  [inline]

Test if the transition function is complete for each state.

Parameters:
a The Boolean automaton to test.
Returns:
true if the transition function of e is complete w.r.t alphabet.
Precondition:
a must be a realtime automaton
See also:
complete(), complete_here()
Author:
Yann Régis-Gianas

Definition at line 95 of file complete.hxx.

References vcsn::is_realtime(), and Element::structure().

Referenced by vcsn::complement_here().

Element< S, T > composition_cover ( const Element< S, T > &  fmp  )  [inline]

Facade for composition cover.

Definition at line 70 of file composition_cover.hxx.

References Element::structure().

Element< A, T > concatenate ( const Element< A, T > &  lhs,
const Element< A, T > &  rhs 
) [inline]

Return the concatenation of two automata.

This function produces a new automata that realizes L(lhs).L(rhs).

Parameters:
lhs The first automaton.
rhs The second automaton.
See also:
concatenate_here()
Returns:
A fresh automaton that is the concatenation of lhs and rhs.

Definition at line 60 of file concatenate.hxx.

References Element::structure().

void concatenate_here ( Element< A, T > &  lhs,
const Element< A, T > &  rhs 
) [inline]

In place concatenation of two automata.

This function modifies lhs to concatenate the language L(rhs) to its language.

It returns the concatenation of two automata using epsilon transitions.

Parameters:
lhs The first automaton.
rhs The second automaton.
See also:
concatenate()
Author:
Yann Regis-Gianas.

Definition at line 69 of file concatenate.hxx.

References Element::structure().

void derived_term_automaton ( Element< A, T > &  a,
const Exp &  e 
) [inline]

Convert a krat expression into an automaton using derivatives.

This algorithm produces an automaton from an expression using the Brzozowski construction. This construction involves multiple derivations on the initial expression.

Parameters:
a An automaton to store the results.
e The expression to convert.
Note:
'a' is generally an empty automaton. It enables the choice of the series to work with. Thus, the series can be different from the expresion ones.

Definition at line 164 of file derived_term_automaton.hxx.

Referenced by vcsn::derived_term_automaton().

Element< A, T > derived_term_automaton ( const Exp &  e  )  [inline]

Convert a krat expression into an automaton using derivatives.

Parameters:
e The expression to convert.
Returns:
A fresh automaton which recognizes the language denoted by 'e'.
Note:
The series of the expression are used to define the automaton.

Definition at line 174 of file derived_term_automaton.hxx.

References vcsn::derived_term_automaton().

Element< A, T > broken_derived_term_automaton ( const Exp &  e  )  [inline]

Convert a krat expression into an automaton using derivatives.

Derivations are first performed on the starting expression with the following formulae: d(0)={0}, d(1)={1}, d(a)={a} for all a in the alphabet, d(E+F)=d(E) union d(F), d(E.F)=[d(E)].F, d(E*)={E*}

Parameters:
e The expression to convert.
Returns:
A fresh automaton which recognizes the language denoted by 'e'.
Note:
The series of the expression are used to define the automaton.

Definition at line 215 of file derived_term_automaton.hxx.

Element< A, T > determinize ( const Element< A, T > &  a  )  [inline]

Returns the determinized of a Boolean automaton.

Parameters:
a The Boolean automaton to determinize.
See also:
ETA p114-117
Precondition:
a must be a Boolean automaton.

a must be a realtime automaton.

Returns:
A fresh Boolean automaton that is the determinization of 'a'.

Definition at line 184 of file determinize.hxx.

Element< A, T > determinize ( const Element< A, T > &  a,
std::map< typename T::hstate_t, std::set< typename T::hstate_t > > &  m 
) [inline]

Returns the determinized of a Boolean automaton.

Parameters:
a The Boolean automaton to determinize.
m A map which will be augmented with the correspondance from one state of the resulting automaton to the set of states of the input automaton.
See also:
ETA p114-117
Precondition:
a must be a Boolean automaton.

a must be a realtime automaton.

Returns:
A fresh Boolean automaton that is the determinization of 'a'.

Definition at line 173 of file determinize.hxx.

References Element::structure().

void eps_removal_here ( Element< A, T > &  a,
misc::direction_type  dir = misc::backward 
) [inline]

In place eps_removal of an automaton (default is backward eps_removal).

This algorithm completes in place the given automaton to make it close over epsilon transition.

It is based on the Floyd/McNaughton/Yamada algorithm.

Parameters:
a The weighted automaton to close.
dir The orientation of the eps_removal.
See also:
eps_removal(), forward_eps_removal(), forward_eps_removal_here(), backward_eps_removal(), backward_eps_removal_here()
Author:
Sylvain Lombardy

Definition at line 432 of file eps_removal.hxx.

References SELECT, and Element::structure().

Referenced by vcsn::do_u_compose().

Element< A, T > eps_removal ( const Element< A, T > &  a,
misc::direction_type  dir = misc::backward 
) [inline]

Eps_Removal of an automaton (default is backward eps_removal).

This algorithm completes the given automaton into a copy to make it close over epsilon transition.

It is based on the Floyd/McNaughton/Yamada algorithm.

Parameters:
a The weighted automaton to close.
dir The orientation of the eps_removal.
See also:
eps_removal_here(), forward_eps_removal(), forward_eps_removal_here(), backward_eps_removal(), backward_eps_removal_here()
Author:
Sylvain Lombardy

Definition at line 444 of file eps_removal.hxx.

References SELECT, and Element::structure().

void backward_eps_removal_here ( Element< A, T > &  a  )  [inline]

In place backward eps_removal of an automaton.

This algorithm completes in place the given automaton to make it close over epsilon transition.

It is based on the Floyd/McNaughton/Yamada algorithm.

Parameters:
a The weighted automaton to close.
See also:
backward_eps_removal(), eps_removal_here(), eps_removal(), forward_eps_removal_here(), forward_eps_removal()
Author:
Sylvain Lombardy

Definition at line 458 of file eps_removal.hxx.

References SELECT, and Element::structure().

Element< A, T > backward_eps_removal ( const Element< A, T > &  a  )  [inline]

Backward eps_removal of an automaton.

This algorithm completes in place the given automaton to make it close over epsilon transition.

It is based on the Floyd/McNaughton/Yamada algorithm.

Parameters:
a The weighted automaton to close.
See also:
backward_eps_removal_here(), eps_removal(), eps_removal_here(), forward_eps_removal(), forward_eps_removal_here()
Author:
Sylvain Lombardy

Definition at line 470 of file eps_removal.hxx.

References SELECT, and Element::structure().

void forward_eps_removal_here ( Element< A, T > &  a  )  [inline]

In place forward eps_removal of an automaton.

This algorithm completes in place the given automaton to make it close over epsilon transition.

It is based on the Floyd/McNaughton/Yamada algorithm.

Parameters:
a The weighted automaton to close.
See also:
forward_eps_removal(), eps_removal_here(), eps_removal(), backward_eps_removal_here(), backward_eps_removal()
Author:
Sylvain Lombardy

Definition at line 484 of file eps_removal.hxx.

References SELECT, and Element::structure().

Element< A, T > forward_eps_removal ( const Element< A, T > &  a  )  [inline]

Forward eps_removal of an automaton.

This algorithm completes in place the given automaton to make it close over epsilon transition.

It is based on the Floyd/McNaughton/Yamada algorithm.

Parameters:
a The weighted automaton to close.
See also:
forward_eps_removal_here(), eps_removal(), eps_removal_here(), backward_eps_removal(), backward_eps_removal_here()
Author:
Sylvain Lombardy

Definition at line 496 of file eps_removal.hxx.

References SELECT, and Element::structure().

void eps_removal_here_sp ( Element< A, T > &  a,
misc::direction_type  dir = misc::backward 
) [inline]

In place eps_removal_sp of an automaton (default is backward eps_removal).

This algorithm completes in place the given automaton to make it close over epsilon transition.

It is based on the shortest-path algorithm.

Parameters:
a The weighted automaton to close.
dir The orientation of the eps_removal.
See also:
eps_removal(), forward_eps_removal(), forward_eps_removal_here(), backward_eps_removal(), backward_eps_removal_here()
Author:
Vivien Delmon

Definition at line 367 of file eps_removal_sp.hxx.

References SELECT, and Element::structure().

Element< A, T > eps_removal_sp ( const Element< A, T > &  a,
misc::direction_type  dir = misc::backward 
) [inline]

Eps_Removal of an automaton (default is backward eps_removal).

This algorithm completes the given automaton into a copy to make it close over epsilon transition.

It is based on the shortest-path algorithm.

Parameters:
a The weighted automaton to close.
dir The orientation of the eps_removal.
See also:
eps_removal_here(), forward_eps_removal(), forward_eps_removal_here(), backward_eps_removal(), backward_eps_removal_here()
Author:
Vivien Delmon

Definition at line 379 of file eps_removal_sp.hxx.

References SELECT, and Element::structure().

void backward_eps_removal_here_sp ( Element< A, T > &  a  )  [inline]

In place backward eps_removal_sp of an automaton.

This algorithm completes in place the given automaton to make it close over epsilon transition.

It is based on the shortest-path algorithm.

Parameters:
a The weighted automaton to close.
See also:
backward_eps_removal(), eps_removal_here(), eps_removal(), forward_eps_removal_here(), forward_eps_removal()
Author:
Vivien Delmon

Definition at line 393 of file eps_removal_sp.hxx.

References SELECT, and Element::structure().

Element< A, T > backward_eps_removal_sp ( const Element< A, T > &  a  )  [inline]

Backward eps_removal_sp of an automaton.

This algorithm completes in place the given automaton to make it close over epsilon transition.

It is based on the shortest-path algorithm.

Parameters:
a The weighted automaton to close.
See also:
backward_eps_removal_here(), eps_removal(), eps_removal_here(), forward_eps_removal(), forward_eps_removal_here()
Author:
Vivien Delmon

Definition at line 405 of file eps_removal_sp.hxx.

References SELECT, and Element::structure().

void forward_eps_removal_here_sp ( Element< A, T > &  a  )  [inline]

In place forward eps_removal_sp of an automaton.

This algorithm completes in place the given automaton to make it close over epsilon transition.

It is based on the shortest-path algorithm.

Parameters:
a The weighted automaton to close.
See also:
forward_eps_removal(), eps_removal_here(), eps_removal(), backward_eps_removal_here(), backward_eps_removal()
Author:
Vivien Delmon

Definition at line 419 of file eps_removal_sp.hxx.

References SELECT, and Element::structure().

Element< A, T > forward_eps_removal_sp ( const Element< A, T > &  a  )  [inline]

Forward eps_removal_sp of an automaton.

This algorithm completes in place the given automaton to make it close over epsilon transition.

It is based on the shortest-path algorithm.

Parameters:
a The weighted automaton to close.
See also:
forward_eps_removal_here(), eps_removal(), eps_removal_here(), backward_eps_removal(), backward_eps_removal_here()
Author:
Vivien Delmon

Definition at line 431 of file eps_removal_sp.hxx.

References SELECT, and Element::structure().

bool are_equivalent ( const Element< S, A > &  a,
const Element< S, B > &  b 
) [inline]

Returns true iff the two boolean automata are equivalents, i.e., if they recognize the same language.

Definition at line 75 of file equivalent.hxx.

References Element::structure().

Element< A, T >::semiring_elt_t eval ( const Element< A, T > &  a,
const W &  word 
) [inline]

Return the image of a word by an automaton.

eval(a, w) returns a series that is the image of the word 'w' in the automaton. This version of computation is the most general one : it works on every types of automaton, deterministic or not. Yet, the automaton must be realtime.

Definition at line 105 of file eval.hxx.

References Element::structure().

identity_transducer_helper< S, T >::ret extension ( const Element< S, T > &  a  )  [inline]

Extend an automaton to a transducer.

Extend an automaton to a transducer whose multiplicity is the series of the automaton.

Definition at line 111 of file extension.hxx.

References Element::structure().

Element< ST, TT > extension ( const Element< SA, TA > &  a,
const Element< ST, TT > &  t 
) [inline]

Extend an automaton to a transducer.

Extend an automaton to a transducer whose set is the one of another transducer passed in the second argument. This extension is required if we want to make a product of an automaton with a transducer. If this is not the case, we need simply call extension(automaton_t) above.

Definition at line 205 of file extension.hxx.

References Element::structure().

void finite_support_convert ( Element< S, T > &  dst,
const Element< Ss, Ts > &  org 
) [inline]

Finite support conversion.

This algorithm copies the value of a finite support application to another, possibly changing its type.

Parameters:
org The source application to convert.
dst The destination application.

Definition at line 31 of file finite_support_conversion.hxx.

References Element::structure().

void forward_realtime_here ( Element< A, T > &  a  )  [inline]

In place modification of the automaton to make it realtime.

Make an automaton realtime, using forward version of eps_removal for building.

Parameters:
a The automaton to make realtime.
See also:
realtime(), forward_realtime(), backward_realtime_here()

Definition at line 38 of file forward_realtime.hxx.

References Element::structure().

Element< A, T > forward_realtime ( const Element< A, T > &  a  )  [inline]

Returns a fresh realtime automaton.

Build a fresh realtime automaton from those given, using forward version of eps_removal.

Parameters:
a The automaton to make realtime.
See also:
realtime(), forward_realtime_here(), backward_realtime()

Definition at line 57 of file forward_realtime.hxx.

References Element::structure().

bool has_succ_comp ( const Element< A, T > &  a  )  [inline]

Return true if the automaton has successful computation (has at least one state that is both accessible and co-accessible), false otherwise.

Definition at line 31 of file has_succ_comp.hxx.

References vcsn::trim().

bool vcsn::is_ambiguous ( const Element< S, A > &  aut  )  [inline]

Test the ambiguity of automaton.

Note:
A trim automaton A is ambiguous if there exists a word f which is the label of two distinct accepting paths A.
Parameters:
aut The automaton to test.
Returns:
true if the automaton is ambiguous.

bool is_deterministic ( const Element< A, T > &  a  )  [inline]

Test if an automaton is deterministic.

Parameters:
a A Boolean automaton.
Precondition:
a is a realtime Boolean automaton.
Returns:
true if 'a' is deterministic.

Definition at line 94 of file is_deterministic.hxx.

Referenced by vcsn::complement_here(), vcsn::minimization_moore(), and vcsn::minimization_moore_here().

bool is_empty ( const Element< A, T > &  a  )  [inline]

Return true if the automaton is empty (has no state), false otherwise.

Definition at line 30 of file is_empty.hxx.

bool is_letterized_transducer ( const Element< S, A > &  t  )  [inline]

Test the letter to letter features.

Parameters:
t The transducer to test.
Returns:
true if the transducer is letter to letter.

Definition at line 50 of file is_letterized.hxx.

References Element::structure().

bool is_normalized_transducer ( const Element< S, A > &  t  )  [inline]

Test the normalization of transducer.

Parameters:
t The transducer to test.
Returns:
true if the transducer is normalized.

Definition at line 50 of file is_normalized.hxx.

References Element::structure().

std::list< typename Series::monoid_t::alphabet_t::letter_t > flatten ( const Element< Series, T > &  exp  )  [inline]

This algorithm extracts the letters from a rational expression.

The flatten() function extracts the letters of a rational expression, keeping the order in which they appear in the expression. The result is just a std::list of letters, with letters having the same type as the expression's letter, i.e. Element<S, T>::monoid_elt_t::set_t::alphabet_t::letter_t.

Parameters:
exp The expression to work on.
Author:
Thomas Claveirole <thomas.claveirole@lrde.epita.fr>

Definition at line 123 of file krat_exp_flatten.hxx.

References KRatExpFlatten::flatten().

Element< A, T > minimization_hopcroft ( const Element< A, T > &  a  )  [inline]

Return the minimal automaton using the hopcroft algorithm.

Minimize a with Hopcroft algorithm.

Parameters:
a The deterministic Boolean automaton to minimize.
Returns:
A fresh automaton that is the canonical minimal automaton of 'a'.
Parameters:
a The automaton.
Precondition:
a Should be deterministic.
Returns:

Definition at line 286 of file minimization_hopcroft.hxx.

References Element::structure().

Element< A, T > quotient ( const Element< A, T > &  a  )  [inline]

Return the quotient of a non-deterministic acceptor.

This algorithms works with both Boolean and weighted automata.

Parameters:
a The automaton to minimize.
Returns:
A fresh automaton that is the quotient of 'a'.
See also:
CIAA 2005, "Inside Vaucanson" (in which the algorithm is described by Sylvain Lombardy)

Definition at line 858 of file minimization_hopcroft.hxx.

References SELECT.

Element< A, T > minimization_moore ( const Element< A, T > &  a  )  [inline]

Returns the minimal deterministic automaton associated to the input one.

Use Moore's algorithm to compute the minimal equivalent deterministic automaton. The complexity of this algorithm is O(n2). See minimize_hopcroft for O(nlogn).

See also:
http://cs.engr.uky.edu/~lewis/essays/compilers/min-fa.html

ETA p123-125

Precondition:
a must be a deterministic Boolean automaton.

Definition at line 239 of file minimization_moore.hxx.

References vcsn::is_deterministic(), and Element::structure().

Element< A, T > co_minimization_moore ( const Element< A, T > &  a  )  [inline]

Returns the co-minimal co-deterministic automaton associated to the input one.

Use Moore's algorithm to compute the minimal equivalent co-deterministic automaton. The complexity of this algorithm is O(n2).

See also:
http://cs.engr.uky.edu/~lewis/essays/compilers/min-fa.html

ETA p123-125

Precondition:
a must be a co-deterministic Boolean automaton.
Bug:
The precondition is not checked.

Definition at line 259 of file minimization_moore.hxx.

References Element::structure().

void minimization_moore_here ( Element< A, T > &  a  )  [inline]

Minimalize the deterministic input automaton.

Use Moore's algorithm to minimalize (in place) the input automaton. The complexity of this algorithm is O(n2). See minimize_hopcroft for O(nlogn).

See also:
http://cs.engr.uky.edu/~lewis/essays/compilers/min-fa.html

ETA p123-125

Precondition:
a must be a deterministic Boolean automaton.

Definition at line 228 of file minimization_moore.hxx.

References vcsn::is_deterministic(), and Element::structure().

void co_minimization_moore_here ( Element< A, T > &  a  )  [inline]

Co-minimalize the co-deterministic input automaton.

Use Moore's algorithm to co-minimalize (in place) the input automaton. The complexity of this algorithm is O(n2). See minimize_hopcroft for O(nlogn).

See also:
http://cs.engr.uky.edu/~lewis/essays/compilers/min-fa.html

ETA p123-125

Precondition:
a must be a co-deterministic Boolean automaton.
Bug:
The precondition is not checked.

Definition at line 249 of file minimization_moore.hxx.

References Element::structure().

Element< A, T > normalize ( const Element< A, T > &  a  )  [inline]

Return the fresh thompson-normalized automaton.

This function returns the thompson-normalized automaton corresponding to its input.

Parameters:
a The automaton to normalize.
See also:
normalize_here(), is_normalized(), union_of_normalized(), concatenate_of_normalized(), star_of_normalized().

Definition at line 62 of file normalized.hxx.

References Element::structure().

void normalize_here ( Element< A, T > &  a  )  [inline]

In-place normalize to the thompson form.

This function performs the in-place thompson-normalization of its input.

Parameters:
a An in/out parameter containing the automaton to normalize as input, and the normalized automaton as output.
See also:
normalize, is_normalized(), union_of_normalized(), concatenate_of_normalized(), star_of_normalized().

Definition at line 71 of file normalized.hxx.

References Element::structure().

bool is_normalized ( const Element< A, T > &  a  )  [inline]

Return true if the input automaton is thompson-normalized.

This function indicates whether its input automaton is thompson-normalized or not.

Parameters:
a The automaton to test.
See also:
normalize(), union_of_normalized(), concatenate_of_normalized(), star_of_normalized().

Definition at line 157 of file normalized.hxx.

References Element::structure().

void union_of_normalized_here ( Element< A, T > &  lhs,
const Element< A, U > &  rhs 
) [inline]

Do the in-place union of two thompson-normalized automata.

This function performs the in-place union of two thompson-normalized automata. The result is thompson-normalized.

Parameters:
lhs An in/out parameter which is the left hand side of the union as input, and the operation result as output.
rhs Right hand side of the union.
See also:
union_of_normalized(), concatenate_of_normalized(), star_of_normalized(), normalize(), is_normalized().

Definition at line 110 of file normalized.hxx.

Element< A, T > union_of_normalized ( const Element< A, T > &  lhs,
const Element< A, U > &  rhs 
) [inline]

Return the fresh union of two thompson-normalized automata.

This function returns a fresh automaton which is the union of input automata. It is thompson-normalized.

Parameters:
lhs Left hand side of the union.
rhs Right hand side of the union.
See also:
union_of_normalized_here(), concatenate_of_normalized(), star_of_normalized(), normalize(), is_normalized().

Definition at line 119 of file normalized.hxx.

References Element::structure().

void concatenate_of_normalized_here ( Element< A, T > &  lhs,
const Element< A, U > &  rhs 
) [inline]

Do the in-place concatenation of two thompson-normalized automata.

This function performs the in-place concatenation of two thompson-normalized automata. The result is thompson-normalized.

Parameters:
lhs An in/out parameter which is the left hand side of the concatenation as input, and the operation result as output.
rhs Right hand side of the concatenation.
See also:
concatenate_of_normalized(), union_of_normalized(), star_of_normalized(), normalize(), is_normalized().

Definition at line 236 of file normalized.hxx.

References Element::structure().

Element< A, T > concatenate_of_normalized ( const Element< A, T > &  lhs,
const Element< A, U > &  rhs 
) [inline]

Return the fresh concatenation of two thompson-normalized automata.

This function returns a fresh automaton which is the concatenation of input automata. It is thompson-normalized.

Parameters:
lhs Left hand side of the concatenation.
rhs Right hand side of the concatenation.
See also:
concatenate_of_normalized_here(), union_of_normalized(), star_of_normalized(), normalize, is_normalized().

Definition at line 244 of file normalized.hxx.

References Element::structure().

void star_of_normalized_here ( Element< A, T > &  a  )  [inline]

Do in-place star transformation on the thompson-normalized input.

This function performs the in-place star transformation of a thompson-normalized automaton. The result is thompson-normalized.

Parameters:
a An in/out parameter which is the automaton to transform as input, and the operation result as output.
See also:
star_of_normalized(), concatenate_of_normalized(), union_of_normalized(), normalize(), is_normalized().

Definition at line 280 of file normalized.hxx.

References Element::structure().

Element< A, T > star_of_normalized ( const Element< A, T > &  a  )  [inline]

Return the fresh star transformation of its normalized input.

This function performs a star transformation on its input, and returns it as a fresh automaton. The input must be thompson-normalized, and the result is thompson-normalized.

Parameters:
a The automaton to run star transformation on.
See also:
star_of_normalized_here(), concatenate_of_normalized(), union_of_normalized(), normalize(), is_normalized().

Definition at line 287 of file normalized.hxx.

References Element::structure().

void compose ( const Element< S, T > &  lhs,
const Element< S, T > &  rhs,
Element< S, T > &  ret 
) [inline]

Composition for weighted normalized and sub-normalized transducers, seen as automata over a free monoid product.

Parameters:
lhs The left hand side transducer.
rhs The right hand side transducer.
ret The result transducer.

Definition at line 425 of file normalized_composition.hxx.

References SELECT, and Element::structure().

Referenced by vcsn::do_compose(), and vcsn::do_u_compose().

Element< S, T > compose ( const Element< S, T > &  lhs,
const Element< S, T > &  rhs 
) [inline]

Composition for weighted normalized and sub-normalized transducers, seen as automata over a free monoid product.

Parameters:
lhs The left hand side transducer.
rhs The right hand side transducer.

Definition at line 445 of file normalized_composition.hxx.

References SELECT, and Element::structure().

void u_compose ( const Element< S, T > &  lhs,
const Element< S, T > &  rhs,
Element< S, T > &  ret 
) [inline]

Unambiguous composition for weighted normalized and sub-normalized transducers, seen as automata over a free monoid product.

Parameters:
lhs The left hand side transducer.
rhs The right hand side transducer.
ret The result transducer.

Definition at line 479 of file normalized_composition.hxx.

References vcsn::do_u_compose(), and Element::structure().

Element< S, T > u_compose ( const Element< S, T > &  lhs,
const Element< S, T > &  rhs 
) [inline]

Unambiguous composition for weighted normalized and sub-normalized transducers, seen as automata over a free monoid product.

Parameters:
lhs The left hand side transducer.
rhs The right hand side transducer.

Definition at line 496 of file normalized_composition.hxx.

References vcsn::do_u_compose(), and Element::structure().

void set_states ( const trans_t &  fmp_trans,
auto_t &  res,
std::map< typename trans_t::hstate_t, typename auto_t::hstate_t > &  stmap 
) [inline]

Definition at line 28 of file projection.hxx.

void vcsn::realtime_here ( Element< A, T > &  a,
misc::direction_type  type 
) [inline]

In place modification of the automaton to make it realtime.

This algorithm makes an automaton realtime. It calls forward_realtime or backward_realtime according type. If type is omitted, forward_realtime is used by default.

Parameters:
a The automaton to make realtime.
type The type of algorithm used.
See also:
realtime(), forward_realtime_here(), backward_realtime_here()

Element< A, T > realtime ( const Element< A, T > &  a,
misc::direction_type  type 
) [inline]

Returns a fresh realtime automaton.

As realtime_here, it build a realtime automaton, but it returns a new one instead of changing the given one.

Parameters:
a The automaton to make realtime.
type The type of algorithm used.
See also:
realtime_here(), forward_realtime(), backward_realtime()

Definition at line 208 of file realtime.hxx.

References Element::structure().

Element< S, T > realtime ( const Element< S, T > &  e  )  [inline]

Calls the do_realtime function for rational expression or automata.

This function is a wrapper which select a realtime either from realtime.hh or from krat_exp_realtime.hh.

When called upon an automaton, this function uses the functions declared in realtime.hh to make this automaton realtime using the forward_realtime() algorithm.

When called with a rational expression, a function from krat_exp_realtime.hh is selected to expand words in the expression as a product of a letter.

See also:
krat_exp_realtime.hh, realtime.hh

Definition at line 26 of file realtime_decl.hxx.

References Element::structure().

void realtime_here ( Element< S, T > &  e  )  [inline]

Calls the do_realtime_here function for rational expression or automata.

This function is a wrapper which select a realtime either from realtime.hh or from krat_exp_realtime.hh.

It behaves exactly as realtime(), but do the operation in place.

See also:
realtime()

Definition at line 33 of file realtime_decl.hxx.

References Element::structure().

bool is_realtime ( const Element< S, T > &  e  )  [inline]

Test whether an automaton or a regular expression is realtime.

This function returns true if the input is realtime.

Parameters:
e The automaton or regular expression to test.
See also:
realtime()

Definition at line 40 of file realtime_decl.hxx.

References Element::structure().

Referenced by vcsn::complete_here(), and vcsn::is_complete().

vcsn::Element< SS, TT > & rw_to_fmp ( const Element< S, T > &  trans,
vcsn::Element< SS, TT > &  res 
) [inline]

Compute the equivalent FMP automaton of a Rational Weight transducer.

Please note that for the moment this function works only if the support of each transition is finite.

Precondition:
trans should use rational weights with finite support.

Definition at line 247 of file rw_to_fmp.hxx.

References Element::structure().

void search ( const Element< Automata< Series >, T > &  a,
const InputIterator &  begin,
const InputIterator &  end,
typename Element< Automata< Series >, T >::letter_t  eol,
FoundFunctor &  f 
) [inline]

Search for a rational expression into a text.

This function searches a rational expression into a text, given a iterator on the text and an automaton which recognizes the corresponding langage. The result cannot spread over two lines.

Parameters:
a The automaton which recognizes the searched words.
begin An input iterator to the begining of the text.
end An iterator to the end of the text.
eol The character to use for ending a line.
f A functor with an operator () method taking 3 InputIterator as argument which will be called each time a match is found. the first one points to the begining of the stream. The two following ones are respectively the first and the last position of the match in the stream.
Authors:
Thomas Claveirole <thomas@lrde.epita.fr>
Bug:
Multiple implementations of search() should be implemented. When a call to search is performed an heuristic should decide which implementation to use. For the moment there is no such mechanism since only one implementation of search is provided.

Definition at line 31 of file search.hxx.

static unsigned int vcsn::compute_distances ( const Element< Automata< Series >, T > &  a,
std::vector< StatesSet > &  distances 
) [inline, static]

Compute distances from initial states to final states.

For each i, compute the set of states reachable in i steps or less. the result is stored into a vector of set of states distances[i]. This algorithm stops when it first encounter a final state. The last i value is returned.

Definition at line 66 of file search.hxx.

References std::swap().

static std::pair<bool, unsigned int> vcsn::window_backsearch ( const misc::Window< InputIterator, typename Element< Automata< Series >, T >::letter_t > &  w,
const Element< Automata< Series >, T > &  a,
const std::vector< StatesSet > &  distances 
) [inline, static]

Back search inside a window.

Returns whether the window is a potential match for the given automaton or not as the first element of the pair. The second element is the maximal value we can use to shift the window without skipping matches.

Parameters:
w The window.
a The automaton to use.
distances Distances get from compute_distances().
See also:
search(), build_reverse_factor_automaton(), compute_distances()

Definition at line 124 of file search.hxx.

References std::swap().

void standardize ( Element< A, T > &  a  )  [inline]

Returns a standard automaton associated to the input.

Parameters:
a The automaton to standardize
See also:
is_standard()

Definition at line 83 of file standard.hxx.

References Element::structure().

bool is_standard ( const Element< A, T > &  a  )  [inline]

Returns true if the input automaton is standard.

Parameters:
a The automaton to test
See also:
standardize()

Definition at line 177 of file standard.hxx.

References Element::structure().

void union_of_standard_here ( Element< A, T > &  lhs,
const Element< A, U > &  rhs 
) [inline]

In-place union of two standard automata.

This function make the union of two standard automata. The result is a standard automaton.

Parameters:
lhs The first automaton (will contain the result)
rhs The second automaton
See also:
standardize(), is_standard(), union_of_standard()

Definition at line 135 of file standard.hxx.

References Element::structure().

Referenced by vcsn::union_of_standard().

Element< A, T > union_of_standard ( const Element< A, T > &  lhs,
const Element< A, U > &  rhs 
) [inline]

Return a fresh union of two standard automata.

As union_of_standard_here, this function build the union of two automatons, but it builds a new one.

Parameters:
lhs The first automaton
rhs The second automaton
See also:
standardize(), is_standard(), union_of_standard_here()

Definition at line 143 of file standard.hxx.

References vcsn::union_of_standard_here().

void concat_of_standard_here ( Element< A, T > &  lhs,
const Element< A, U > &  rhs 
) [inline]

In-place concatenation of two standard automata.

This function make the concatenation of two standard automata. The result is a standard automaton.

Parameters:
lhs The first automaton (will contain the result)
rhs The second automaton
See also:
standardize(), is_standard(), concat_of_standard()

Definition at line 263 of file standard.hxx.

Element< A, T > concat_of_standard ( const Element< A, T > &  lhs,
const Element< A, U > &  rhs 
) [inline]

Return a fresh concatenation of two standard automata.

As concat_of_standard_here, this function build the union of two automatons, but it builds a new one.

Parameters:
lhs The first automaton
rhs The second automaton
See also:
standardize(), is_standard(), concat_of_standard_here()

Definition at line 271 of file standard.hxx.

References Element::structure().

void star_of_standard_here ( Element< A, T > &  a  )  [inline]

In-place star transformation of a standard automata.

This function make the star transformation of a standard automaton, and replace those given by the result.

Parameters:
a The automaton to transform
See also:
standardize(), is_standard(), star_of_standard()

Definition at line 314 of file standard.hxx.

Element< A, T > star_of_standard ( const Element< A, T > &  a  )  [inline]

Return the fresh star transformation of a standard automata.

As star_of_standard_here, this function applies star on an automaton, but it build a new automaton.

Parameters:
a The automaton on which star must be applied.
See also:
standardize(), is_standard(), star_of_standard_here()

Definition at line 321 of file standard.hxx.

References Element::structure().

void standard_of ( Element< A, T > &  a,
const Exp &  e 
) [inline]

Convert a rational expression into a standard automaton.

Parameters:
e The expression to convert.
a The automaton to store the result.
Note:
The automaton is used to enable the use of different series from the expression.

Definition at line 228 of file standard_of.hxx.

References Element::structure().

Element< A, T > sub_automaton ( const Element< A, T > &  a,
const StatesSet &  s,
bool  check_states = true 
) [inline]

Returns a fresh automaton that is the sub-automaton defined by a set.

Parameters:
a The automaton into which we have to extract the sub-automaton.
s The set of states of the sub-automaton included in the state of 'a'.
check_states A flag to enable/disable the inclusion checking.
Returns:
A fresh sub-automaton.
See also:
sub_automaton_here()

Definition at line 58 of file sub_automaton.hxx.

References Element::structure().

Referenced by vcsn::accessible(), vcsn::coaccessible(), and vcsn::trim().

void sub_automaton_here ( Element< A, T > &  a,
const StatesSet &  s,
bool  check_states = true 
) [inline]

Select a sub-automaton into a given automaton.

Parameters:
a The automaton into which we have to extract the sub-automaton.
s The set of states of the sub-automaton included in the state of 'a'.
check_states A flag to enable/disable the inclusion checking.
See also:
sub_automaton()

Definition at line 71 of file sub_automaton.hxx.

References Element::structure().

Referenced by vcsn::accessible_here(), vcsn::coaccessible_here(), vcsn::do_u_compose(), and vcsn::trim_here().

Element< S, T > sub_normalize ( const Element< S, T > &  a  )  [inline]

Sub-normalize a FMP transducer.

  • a Input automaton.
    Returns:
    Sub-normalized automaton.

Definition at line 220 of file sub_normalize.hxx.

void vcsn::sub_normalize ( const Element< S, T1 > &  a,
Element< S, T2 > &  res 
) [inline]

Sub-normalize a FMP transducer.

  • a Input automaton.
  • res Output automaton.

void sub_normalize_here ( Element< S, T > &  a  )  [inline]

Sub-normalize a FMP transducer, in place version.

Parameters:
a Input automaton.

Definition at line 238 of file sub_normalize.hxx.

References Element::structure().

bool is_sub_normalized ( const Element< S, T > &  a  )  [inline]

Check if a FMP transducer is sub-normalized.

  • a Input automaton.
    Returns:
    boolean.

Definition at line 244 of file sub_normalize.hxx.

References Element::structure().

void sum_here ( Element< A, T > &  lhs,
const Element< A, U > &  rhs 
) [inline]

In place summing of two automata.

This function adds states and transitions of an automaton to states and transitions of a second automaton.

Parameters:
lhs Destination of the summing
rhs Source of summing
See also:
sum()

Definition at line 86 of file sum.hxx.

References Element::structure().

Element< A, T > sum ( const Element< A, T > &  lhs,
const Element< A, U > &  rhs 
) [inline]

Summing of two automata.

This function returns the fresh union of two automata. It put transitions and states of the two automata together, and create a news one with the result.

Parameters:
lhs First automaton to sum
rhs Second automaton to sum
See also:
sum_here()

Definition at line 94 of file sum.hxx.

References Element::structure().

void thompson_of ( Element< A, T > &  out,
const rat::exp< Letter, Weight > &  kexp 
) [inline]

The Thompson automaton associated to the krat expression.

This function build the automaton associated to the rational expression implemented by a krat_exp, using Thompson algorithm.

Parameters:
out The resulting automaton
kexp The rational expression

Definition at line 209 of file thompson.hxx.

References Element::structure().

Referenced by vcsn::thompson_of().

Element< Automata< S >, AutoType > thompson_of ( const Element< S, T > &  exp  )  [inline]

The Thompson automaton associated to the krat expression.

This function build the automaton associated to the rational expression implemented by a krat_exp, using Thompson algorithm. The kind of returned automaton is a default one.

Parameters:
exp The rational expression

Definition at line 217 of file thompson.hxx.

References Element::structure(), vcsn::thompson_of(), and Element::value().

void transpose ( lhs_t &  dst,
const rhs_t &  from 
) [inline]

Transposition of an automaton.

This function copy in dst the transposition of the automaton from.

Parameters:
from Automaton to transpose
dst Destination

Definition at line 29 of file algorithms/transpose.hxx.

References vcsn::transpose_view().

auto_t transpose ( const auto_t &  from  )  [inline]

Return a fresh transposed automaton.

This function returns the transposition of an automaton.

Parameters:
from Automaton to transpose.

Definition at line 42 of file algorithms/transpose.hxx.

References vcsn::transpose().

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