The main namespace of the Vaucanson library. More...

Namespaces
namespace	algebra
	Namespace for algebra constructs in Vaucanson.
namespace	delta_kind
	These are helpers for `delta` functions: transition or state oriented delta are chosen according to them.
namespace	misc
	The namespace for miscellaneous constructs.
Classes
struct	dynamic_traits< algebra::AlphabetSetBase< S > >
	Specialization of `dynamic_traits` for `AlphabetSetBase`. More...
struct	virtual_types< algebra::AlphabetSetBase< S > >
	Specialization of `virtual_types` for `AlphabetSetBase`. More...
struct	MetaElement< algebra::AlphabetSetBase< S >, T >
	Specialization of `MetaElement` for `AlphabetSetBase`. More...
struct	dynamic_traits< algebra::CyclicSemiring< n > >
	Meta information about the cyclic semirings. More...
struct	MetaElement< algebra::CyclicSemiring< n >, T >
	Services of element of a tropical semiring. More...
struct	dynamic_traits< algebra::FreeMonoidBase< Self > >
struct	MetaElement< algebra::FreeMonoidBase< Self >, T >
	Element of a free monoid i.e. words. More...
struct	dynamic_traits< algebra::FreeMonoidProduct< F, S > >
	Meta information about FreeMonoidProduct. More...
struct	MetaElement< algebra::FreeMonoidProduct< F, S >, T >
	Services of an element of a monoid implemented with FreeMonoidProduct. More...
struct	dynamic_traits< algebra::FreeMonoidProductBase< Self > >
struct	MetaElement< algebra::FreeMonoidProductBase< Self >, T >
	Element of a monoid i.e. words. More...
struct	dynamic_traits< algebra::MonoidBase< Self > >
struct	MetaElement< algebra::MonoidBase< Self >, T >
	Defines services of element of every monoid. More...
struct	dynamic_traits< algebra::NumericalSemiring >
	Meta information about the NumericalSemiring structural element. More...
struct	MetaElement< algebra::NumericalSemiring, T >
	Services of `Element` for numerical semirings. More...
struct	dynamic_traits< algebra::SemigroupBase< Self > >
struct	MetaElement< algebra::SemigroupBase< Self >, T >
	Services of every element of a semigroup. More...
struct	dynamic_traits< algebra::SemiringBase< Self > >
struct	MetaElement< algebra::SemiringBase< Self >, T >
	Services of every element of semiring (semiring_elt). More...
struct	op_star_traits
	Meta information about the return type of the star operation. More...
struct	semiring_traits
	Is the semiring positive? More...
struct	dynamic_traits< algebra::SeriesBase< Self > >
class	MetaElement< algebra::SeriesBase< Self >, T >
	Services of every series. More...
struct	dynamic_traits< algebra::TropicalSemiring< TropicalKind > >
	Meta information about the tropical semirings. More...
struct	MetaElement< algebra::TropicalSemiring< TropicalKind >, T >
	Services of element of a tropical semiring. More...
struct	MetaElement< algebra::AlphabetSet< L >, std::set< L > >
	Services of every alphabet implemented with std::set. More...
struct	dynamic_traits< algebra::AlphabetSet< L > >
	Meta information about AlphabetSet. More...
struct	MetaElement< algebra::AlphabetSet< L >, algebra::AlphabetDecorator< L, T > >
	Services of every alphabet implemented with AlphabetDecorator<L, T>. More...
struct	dynamic_traits< algebra::FreeMonoid< A > >
	Meta information about FreeMonoid. More...
struct	MetaElement< algebra::FreeMonoid< A >, T >
	Services of an element of a free monoid implemented with FreeMonoid. More...
struct	MetaElement< algebra::Series< W, M >, T >
	Specialization of MetaElement for series. More...
struct	dynamic_traits< algebra::Series< W, M > >
	Dynamic traits for series. More...
struct	virtual_types< algebra::Series< W, M > >
	Virtual types for series. More...
struct	KRatExpAciCanonical
	Visitor to build a canonical form of an expression, following aci-rules. More...
struct	DefaultChooser
	Default chooser for aut_to_exp(). More...
struct	RandomChooser
	Choose randomly a state between all currently choosable. More...
struct	DMChooser
	Choose a state accordingly to an heuristic. More...
class	ListChooser
	Chooser for aut_to_exp(). More...
struct	BerrySethiAlgo
	This is the visitor that really computes Berry-Sethi. More...
struct	BrzozowskiAlgo
	This is the class that really computes Brzozowski. More...
struct	KRatExpInitialDerivation
	Visitor to have an initial set of partial derivatives terms from an expression. More...
class	PRatExpDerivationVisitor
	This class performs partial rational expression derivations. More...
class	ConstantTermEval
	This is the visitor that really computes the constant term. More...
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...
struct	dynamic_traits< Automata< Series, Kind > >
	Dynamic traits for automata. More...
struct	MetaElement< Automata< Series, Kind >, T >
	MetaElement specialization for automata. More...
struct	virtual_types< Automata< Series, Kind > >
	Virtual types for automata. More...
class	Automata
	Final class for the set of automata. More...
struct	AutomataBase
	The most general concept of automaton. More...
struct	MetaElement< AutomataBase< Self >, T >
	Services of every element of the automata set. More...
class	AutoKind< labels_are_series, Self, Series, SeriesT, LabelT >
	Add adapted accessors in function of the automaton kind. More...
struct	dynamic_traits< Transducer< Series, Kind > >
	Dynamic traits for transducers. More...
struct	MetaElement< Transducer< Series, Kind >, T >
	Specialization of MetaElement for transducers. More...
struct	virtual_types< Transducer< Series, Kind > >
	Virtual types for transducers. More...
class	Transducer
	Final class for the set of transducers. More...
struct	TransducerBase
	The most general concept of transducer. More...
struct	transducer_traits
	Traits for transducer implementation. More...
struct	MetaElement< TransducerBase< Self >, T >
	Services of every element of the transducer set. More...
struct	geometry
	Store 4 maps for geometry properties of the automaton. More...
struct	TransposeView
	Provides a transposed view of an automaton. More...
struct	transpose_traits
	Traits for TransposeView. More...
struct	automaton_traits< TransposeView< T > >
	automaton_traits specialization for the TransposeView implementation. More...
class	Element
	Glue class between structural elements and implementation values. More...
struct	op_add_traits
	The type of the result of addition between two Element instances. More...
struct	op_sub_traits
	The type of the result of substraction between two Element instances. More...
struct	op_mul_traits
	The type of the result of multiplication between two Element instances. More...
struct	op_div_traits
	The type of the result of division between two Element instances. More...
struct	op_mod_traits
	The type of the result of modulus between two Element instances. More...
struct	MetaElement< Structure< S >, T >
	The base class that glues structural elements to implementation values. More...
struct	SetSlotAttribute
	Base class for `SetSlot`. More...
struct	SetSlotAttribute< S, true >
	Base class for `SetSlot`, specializing `SetSlotAttribute`. More...
struct	SetSlot
	Type of the `set_` attribute of the `Element` class. More...
struct	Structure
	Base class for the hierarchy of structural element types. More...
struct	dynamic_traits< Structure< S > >
	Specialization of `dynamic_traits` for `Structure`. More...
struct	virtual_types< Structure< S > >
	Specialization of `virtual_types` for `Structure`. More...
struct	SyntacticDecorator
	Provides the standard operator delegations to Element. More...
Enumerations
enum	op_choose_max_word_length_t
	Maximum length of words generated by op_choose. More...
Functions
template<typename S , typename T >
std::pair< bool, typename Element< S, T >::letter_t >	parse_letter (const Element< S, T > &alphabet, const std::string &s)
	Public interface to the letter parser.
template<typename S , typename T >
Element< S, T >	mirror (const Element< S, T > &e)
	Return a fresh word that is the mirror.
template<typename S , typename T >
std::pair< bool, int >	parse_word (Element< S, T > &dest, const std::string &s)
	Parse the beginning of the string looking for a word.
template<typename S , typename T >
op_star_traits< S, T >::ret_t	star (const Element< S, T > &w)
	Returns a fresh weight that is the star of w.
template<typename S , typename T >
bool	parse_weight (Element< S, T > &w, const std::string &, typename std::string::const_iterator &)
	Parse the beginning of the string looking for a weight.
template<typename S , typename T >
bool	starable (const Element< S, T > &elt)
	Returns true if we can compute the star of the weight.
template<typename S , typename T >
Element< S, T >	transpose (const algebra::SeriesBase< S > &s, const T &t)
	returns a fresh series that is the transposed of the argument.
template<typename S , typename T >
bool	is_support_in_alphabet (const Element< S, T > &s)
	Returns true if the support of the series is only composed of letters.
template<typename S1 , typename S2 , typename T1 , typename T2 >
void	extract_support (Element< S1, T1 > &, Element< S2, T2 > &)
	Make the first series be the support of the second.
template<class S , class T >
Element< S, T >	hadamard (const Element< S, T > &lhs, const Element< S, T > &rhs)
	Return the hadamard product of lhs and rhs.
template<typename A , typename AI >
std::set< typename Element< A, AI >::hstate_t >	accessible_states (const Element< A, AI > &a)
	Return accessible states.
template<typename A , typename AI >
Element< A, AI >	accessible (const Element< A, AI > &a)
	Extract the sub-automaton composed of accessible states.
template<typename A , typename AI >
void	accessible_here (Element< A, AI > &a)
	In-place extract the sub-automaton of accessible states.
template<typename A , typename AI >
std::set< typename Element< A, AI >::hstate_t >	coaccessible_states (const Element< A, AI > &a)
	Return co-accessible states.
template<typename A , typename AI >
Element< A, AI >	coaccessible (const Element< A, AI > &a)
	Extract the sub-automaton composed of co-accessible states.
template<typename A , typename AI >
void	coaccessible_here (Element< A, AI > &a)
	In-place extract the sub-automaton of co-accessible states.
template<typename S , typename SI >
Element< S, SI >	canonical (const Element< S, SI > &exp)
	Transform a krat expression into a canonical form using only ACI-rules.
template<typename A , typename AI >
Element< A, AI >::series_set_elt_t	aut_to_exp (const Element< A, AI > &a)
	Returns a series which describes the language of the automaton.
template<typename A , typename AI , typename Chooser >
Element< A, AI >::series_set_elt_t	aut_to_exp (const Element< A, AI > &a, const Chooser &c)
	Returns a series which describes the language of the 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 S , typename T >
linearize_element< S, T > ::alphabet_t	linearized_alphabet (const Element< S, T > &exp)
	Computes a linearized alphabet from a rational expression.
template<typename Exp , typename Letter >
Exp	linear_exp_continuation (const Exp &exp, const Letter &l)
	This function computes a continuation on linearized expressions.
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 lhs_t , typename rhs_t >
void	characteristic (lhs_t &dst, const rhs_t &from)
	Build a characteristic automaton.
template<typename A , typename AI >
void	complement_here (Element< A, AI > &a)
	Complement in place the set of final states.
template<typename A , typename AI >
Element< A, AI >	complement (const Element< A, AI > &a)
	Complement the set of final states.
template<typename A , typename AI >
void	complete_here (Element< A, AI > &a)
	Make the transition function of an automaton total w.r.t.
template<typename A , typename AI >
Element< A, AI >	complete (const Element< A, AI > &a)
	Make the transition function of an automaton total w.r.t.
template<typename A , typename AI >
bool	is_complete (const Element< A, AI > &a)
	Test whether an automaton is complete.
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<typename A , typename AI >
bool	is_cut_up (const Element< A, AI > &a)
	Check if labels are series with one element.
template<typename A , typename AI >
Element< A, AI >	cut_up (const Element< A, AI > &a)
	Transform an automaton labeled with series to an automaton where all labels are series with one and only one element.
template<typename A , typename AI >
void	cut_up (const Element< A, AI > &a, Element< A, AI > &res)
	Transform an automaton labeled with series to an automaton where all labels are series with one and only one element.
template<typename A , typename AI >
void	cut_up_here (Element< A, AI > &a)
	Transform an automaton labeled with series to an automaton where all labels are series with one and only one element.
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 AI >
bool	is_proper (const Element< A, AI > &a)
	Test whether an automaton is proper.
template<typename A , typename AI >
void	eps_removal_here (Element< A, AI > &a, misc::direction_type dir=misc::backward)
	In place eps_removal of an automaton (default is backward eps_removal).
template<typename A , typename AI >
Element< A, AI >	eps_removal (const Element< A, AI > &a, misc::direction_type dir=misc::backward)
	Eps_Removal of an automaton (default is backward eps_removal).
template<typename A , typename AI >
void	backward_eps_removal_here (Element< A, AI > &a)
	In place backward eps_removal of an automaton.
template<typename A , typename AI >
Element< A, AI >	backward_eps_removal (const Element< A, AI > &a)
	Backward eps_removal of an automaton.
template<typename A , typename AI >
void	forward_eps_removal_here (Element< A, AI > &a)
	In place forward eps_removal of an automaton.
template<typename A , typename AI >
Element< A, AI >	forward_eps_removal (const Element< A, AI > &a)
	Forward eps_removal of an automaton.
template<typename A , typename AI >
void	eps_removal_here_sp (Element< A, AI > &a, misc::direction_type dir=misc::backward)
	In place eps_removal_sp of an automaton (default is backward eps_removal).
template<typename A , typename AI >
Element< A, AI >	eps_removal_sp (const Element< A, AI > &a, misc::direction_type dir=misc::backward)
	Eps_Removal of an automaton (default is backward eps_removal).
template<typename A , typename AI >
void	backward_eps_removal_here_sp (Element< A, AI > &a)
	In place backward eps_removal_sp of an automaton.
template<typename A , typename AI >
Element< A, AI >	backward_eps_removal_sp (const Element< A, AI > &a)
	Backward eps_removal_sp of an automaton.
template<typename A , typename AI >
void	forward_eps_removal_here_sp (Element< A, AI > &a)
	In place forward eps_removal_sp of an automaton.
template<typename A , typename AI >
Element< A, AI >	forward_eps_removal_sp (const Element< A, AI > &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 AI , typename W >
Element< A, AI >::semiring_elt_t	eval (const Element< A, AI > &a, const W &word)
	Return the image of a word by an automaton.
template<typename ST , typename TT >
void	evaluation_fmp (const Element< ST, TT > &trans, const typename input_projection_helper< ST, TT >::ret &aut, typename output_projection_helper< ST, TT >::ret &res)
	Evaluation over normalized and sub-normalized transducers, seen as automata over a free monoid product.
template<typename SA , typename TA , typename ST , typename TT , typename SRET , typename TRET >
void	evaluation_rw (const Element< SA, TA > &a, const Element< ST, TT > &t, Element< SRET, TRET > &ret)
	Evaluate for a "letterized" automaton and a realtime transducer.
template<typename S , typename K , typename T >
identity_transducer_helper< S, K, 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 A , typename AI >
void	factor_here (const Element< A, AI > &a)
	Make every states of the automaton initial and final states (in place).
template<typename A , typename AI >
Element< A, AI >	factor (const Element< A, AI > &a)
	Make every states of the automaton initial and final states.
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<class S , class T >
output_projection_helper< S, T > ::ret	image (const Element< S, T > &)
template<typename SA , typename TA , typename M >
void	partial_elimination (const Element< SA, TA > &a, M &state_exp_pair)
	This function computes a set of expression, after having eliminated all states which are not initial or final.
template<typename S1 , typename T1 , typename S2 , typename T2 , typename M >
void	partial_evaluation (const Element< S1, T1 > &E, const Element< S2, T2 > &S, const typename Element< S2, T2 >::hstate_t &p, M &res)
	Partial evaluation of a K RatExp E over a realtime transducer S, starting from a given state p.
template<typename A , typename T >
bool	has_successors (const Element< A, T > &a, const typename automaton_traits< T >::hstate_t s)
	Whether a state has successors.
template<typename A , typename T >
bool	has_predecessors (const Element< A, T > &a, const typename automaton_traits< T >::hstate_t s)
	Whether a state has predecessors.
template<typename A , typename T >
void	invert (const Element< A, T > &t, Element< A, T > &res)
	Invert a transducer.
template<typename A , typename T >
Element< A, T > &	invert (const Element< A, T > &t)
	Invert a transducer.
template<typename A , typename AI >
bool	is_ambiguous (const Element< A, AI > &aut)
	Test the ambiguity of automaton.
template<typename A , typename AI >
bool	is_deterministic (const Element< A, AI > &a)
	Test if an automaton is deterministic.
template<typename A , typename AI >
bool	is_empty (const Element< A, AI > &a)
	Evaluate if an automaton is empty.
template<typename S , typename A >
bool	is_ltl (const Element< S, A > &t)
	Test whether an FMP transducer is letter-to-letter.
template<typename S , typename A >
bool	is_normalized_transducer (const Element< S, A > &t)
	Test the normalization of transducer.
template<typename A , typename AI >
bool	is_trim (const Element< A, AI > &a)
	Return true is all states are reachable and co-reachable.
template<typename A , typename AI >
bool	is_useless (const Element< A, AI > &a)
	Return true if the automaton has no successful computation.
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 AI >
Element< A, AI >	minimization_hopcroft (const Element< A, AI > &a)
	Return the minimal automaton using the hopcroft algorithm.
template<typename A , typename AI >
Element< A, AI >	quotient (const Element< A, AI > &a)
	Return the quotient of a non-deterministic acceptor.
template<typename A , typename AI >
Element< A, AI >	minimization_moore (const Element< A, AI > &a)
	Returns the minimal deterministic automaton associated to the input one.
template<typename A , typename AI >
Element< A, AI >	co_minimization_moore (const Element< A, AI > &a)
	Returns the co-minimal co-deterministic automaton associated to the input one.
template<typename A , typename AI >
void	minimization_moore_here (Element< A, AI > &a)
	Minimalize the deterministic input automaton.
template<typename A , typename AI >
void	co_minimization_moore_here (Element< A, AI > &a)
	Co-minimalize the co-deterministic input automaton.
template<typename A , typename AI >
Element< A, AI >	normalize (const Element< A, AI > &a)
	Return the fresh thompson-normalized automaton.
template<typename A , typename AI >
void	normalize_here (Element< A, AI > &a)
	In-place normalize to the thompson form.
template<typename A , typename AI >
bool	is_normalized (const Element< A, AI > &a)
	Return true if the input automaton is thompson-normalized.
template<typename A , typename AI1 , typename AI2 >
void	union_of_normalized_here (Element< A, AI1 > &lhs, const Element< A, AI2 > &rhs)
	Do the in-place union of two thompson-normalized automata.
template<typename A , typename AI1 , typename AI2 >
Element< A, AI1 >	union_of_normalized (const Element< A, AI1 > &lhs, const Element< A, AI2 > &rhs)
	Return the fresh union of two thompson-normalized automata.
template<typename A , typename AI1 , typename AI2 >
void	concatenate_of_normalized_here (Element< A, AI1 > &lhs, const Element< A, AI2 > &rhs)
	Do the in-place concatenation of two thompson-normalized automata.
template<typename A , typename AI1 , typename AI2 >
Element< A, AI1 >	concatenate_of_normalized (const Element< A, AI1 > &lhs, const Element< A, AI2 > &rhs)
	Return the fresh concatenation of two thompson-normalized automata.
template<typename A , typename AI >
void	star_of_normalized_here (Element< A, AI > &a)
	Do in-place star transformation on the thompson-normalized input.
template<typename A , typename AI >
Element< A, AI >	star_of_normalized (const Element< A, AI > &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 S , typename M1 , typename M2 , typename lhs_t , typename rhs_t , typename res_t >
void	do_compose (const AutomataBase< S > &, const algebra::FreeMonoidProduct< M1, M2 > &, const lhs_t &lhs, const rhs_t &rhs, res_t &ret)
	Ambiguous composition.
template<typename S , typename M1 , typename M2 , typename lhs_t , typename rhs_t , typename res_t >
void	do_u_compose (const AutomataBase< S > &, const algebra::FreeMonoidProduct< M1, M2 > &, const lhs_t &lhs, const rhs_t &rhs, res_t &ret)
	Unambiguous composition.
template<typename A , typename AI , typename EPS >
void	one_eps_closure (Element< A, AI > &a, const EPS &eps, misc::direction_type dir=misc::backward)
	In place one_eps_closure of an automaton (default is backward eps_closure).
template<typename A , typename AI , typename EPS >
void	backward_one_eps_closure (Element< A, AI > &a, const EPS &eps)
	In place backward_one_eps_closure of an automaton.
template<typename A , typename AI , typename EPS >
void	forward_one_eps_closure (Element< A, AI > &a, const EPS &eps)
	In place forward one_eps_closure of an automaton.
template<typename A , typename AI >
void	prefix_here (const Element< A, AI > &a)
	Make every states of the automaton final states (in place).
template<typename A , typename AI >
Element< A, AI >	prefix (const Element< A, AI > &a)
	Make every states of the automaton final states.
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 AI >
void	realtime_here (Element< A, AI > &a, misc::direction_type dir)
	Modify an automaton in place to make it realtime.
template<typename A , typename AI >
Element< A, AI >	realtime (const Element< A, AI > &a, misc::direction_type dir)
	Create a realtime automaton from another one.
template<typename S , typename T >
Element< S, T >	realtime (const Element< S, T > &e)
	Compute the realtime version of a rational expression or an automata.
template<typename S , typename T >
void	realtime_here (Element< S, T > &e)
	Modify a rational expression or automata in place to make it realtime.
template<typename S , typename T >
bool	is_realtime (const Element< S, T > &e)
	Test whether an automaton or a rational expression is realtime.
template<typename A , typename AI >
Element< A, AI >	reduce (const Element< A, AI > &a, misc::direction_type dir=misc::right_left)
	Reduce of an automaton (default right_left).
template<typename A , typename AI >
Element< A, AI >	semi_reduce (const Element< A, AI > &a)
	Semi reduction of an automaton.
template<typename S , typename T >
void	rw_composition (const Element< S, T > &lhs, const Element< S, T > &rhs, Element< S, T > &ret)
	Composition for Rational-Weight transducers.
template<typename S , typename T >
Element< S, T >	rw_composition (const Element< S, T > &lhs, const Element< S, T > &rhs)
	Composition for Rational-Weight transducers.
template<typename InputIterator , typename FoundFunctor , typename Series , typename Kind , typename T >
void	search (const Element< Automata< Series, Kind >, T > &a, const InputIterator &begin, const InputIterator &end, typename Element< Automata< Series, Kind >, T >::letter_t eol, FoundFunctor &f)
	Search for a rational expression into a text.
template<typename Series , typename Kind , typename T , typename StatesSet >
static unsigned int	compute_distances (const Element< Automata< Series, Kind >, T > &a, std::vector< StatesSet > &distances)
	Compute distances from initial states to final states.
template<typename InputIterator , typename Series , typename Kind , typename T , typename StatesSet >
static std::pair< bool, unsigned int >	window_backsearch (const misc::Window< InputIterator, typename Element< Automata< Series, Kind >, T >::letter_t > &w, const Element< Automata< Series, Kind >, T > &a, const std::vector< StatesSet > &distances)
	Back search inside a window.
template<typename InputIterator , typename FoundFunctor , typename Series , typename Kind , typename T >
static InputIterator	confirm_and_report_match (const misc::Window< InputIterator, typename Element< Automata< Series, Kind >, T >::letter_t > &w, const Element< Automata< Series, Kind >, T > &a, FoundFunctor &f)
	Finds the longest match of a starting from w, and report it to the functor.
template<typename Automaton >
Automaton::monoid_elt_t	shortest (const Automaton &autom)
	Return the smallest accepted word.
template<typename Automaton , typename MonoidElt >
bool	shortest (const Automaton &autom, MonoidElt &word)
	Compute the smallest accepted word.
template<typename Automaton , typename MonoidElt , typename Alloc >
void	enumerate (const Automaton &autom, unsigned max_length, std::list< MonoidElt, Alloc > &word_list)
	Compute the list of short accepted words.
template<typename A , typename AI1 , typename AI2 >
void	union_here (Element< A, AI1 > &lhs, const Element< A, AI2 > &rhs)
	In place union of two automata.
template<typename A , typename AI1 , typename AI2 >
Element< A, AI1 >	union_ (const Element< A, AI1 > &lhs, const Element< A, AI2 > &rhs)
	Union of two automata.
template<typename A , typename AI >
bool	is_standard (const Element< A, AI > &a)
	Returns true iff the input automaton is standard.
template<typename A , typename AI >
void	standardize (Element< A, AI > &a)
	Returns a standard automaton associated to the input.
template<typename A , typename AI1 , typename AI2 >
void	sum_of_standard_here (Element< A, AI1 > &lhs, const Element< A, AI2 > &rhs)
	In-place sum of two standard automata.
template<typename A , typename AI1 , typename AI2 >
Element< A, AI1 >	sum_of_standard (const Element< A, AI1 > &lhs, const Element< A, AI2 > &rhs)
	Return a fresh sum of two standard automata.
template<typename A , typename AI1 , typename AI2 >
void	concat_of_standard_here (Element< A, AI1 > &lhs, const Element< A, AI2 > &rhs)
	In-place concatenation of two standard automata.
template<typename A , typename AI1 , typename AI2 >
Element< A, AI1 >	concat_of_standard (const Element< A, AI1 > &lhs, const Element< A, AI2 > &rhs)
	Return a fresh concatenation of two standard automata.
template<typename A , typename AI >
void	star_of_standard_here (Element< A, AI > &a)
	In-place star transformation of a standard automaton.
template<typename A , typename AI >
Element< A, AI >	star_of_standard (const Element< A, AI > &a)
	Return the fresh star transformation of a standard automata.
template<typename A , typename AI >
void	left_mult_of_standard_here (Element< A, AI > &aut, const typename Element< A, AI >::series_set_elt_t &k)
	In-place left exterior multiplication by a weight.
template<typename A , typename AI >
void	right_mult_of_standard_here (Element< A, AI > &aut, const typename Element< A, AI >::series_set_elt_t &k)
	In-place right exterior multiplication by a weight.
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 AI , typename HStatesSet >
Element< A, AI >	sub_automaton (const Element< A, AI > &a, const HStatesSet &s, bool check_states=true)
	Returns a fresh automaton that is the sub-automaton defined by a set.
template<typename A , typename AI , typename HStatesSet >
void	sub_automaton_here (Element< A, AI > &a, const HStatesSet &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 AI >
void	suffix_here (const Element< A, AI > &a)
	Make every states of the automaton initial states (in place).
template<typename A , typename AI >
Element< A, AI >	suffix (const Element< A, AI > &a)
	Make every states of the automaton initial states.
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<typename AutoType , typename S , typename K , class T >
Element< Automata< S, K > , AutoType >	thompson_of (const Element< S, T > &exp)
	The Thompson automaton associated to the krat expression.
template<typename A , typename AI1 , typename AI2 >
void	transpose (Element< A, AI1 > &dst, const Element< A, AI2 > &src)
	Transposition of an automaton.
template<typename A , typename AI >
Element< A, AI >	transpose (const Element< A, AI > &src)
	Return a fresh transposed automaton.
template<typename A , typename AI >
std::set< typename Element< A, AI >::hstate_t >	useful_states (const Element< A, AI > &a)
	Returns a useful states of the automaton.
template<typename A , typename AI >
Element< A, AI >	trim (const Element< A, AI > &a)
	Return a fresh automaton in which non useful states are removed.
template<typename A , typename AI >
void	trim_here (Element< A, AI > &a)
	Trim a.
template<typename lhs_t , typename rhs_t , typename F >
void	auto_translate_transitions (lhs_t &dst, const rhs_t &from, const F &translate_fun)
template<typename S , typename T >
bool	op_contains (const Structure< S > &set, const T &value)
	Check whether a value is contained in a set.
template<typename S , typename T , typename U >
bool	op_eq (const Structure< S > &, const T &v1, const U &v2)
	Equality between two structured values.
template<typename S , typename V , typename T , typename U >
bool	op_eq (const Structure< S > &, const Structure< V > &, const T &v1, const U &v2)
	Equality between two structured values.
template<typename S , typename T , typename U >
bool	op_lt (const Structure< S > &, const T &v1, const U &v2)
	Ordered comparison between two structured values.
template<typename S , typename V , typename T , typename U >
bool	op_lt (const Structure< S > &, const Structure< V > &, const T &v1, const U &v2)
	Ordered comparison between two structured values.
template<typename S , typename R , typename T >
R	op_convert (const Structure< S > &se, SELECTOR(R), const T &data)
	Default conversion between value types with computation.
template<typename S , typename T >
const T &	op_convert (const Structure< S > &se, SELECTOR(T), const T &from_data)
	Pass-through conversion.
template<typename S , typename T >
const T &	op_convert (const Structure< S > &se, SELECTOR(T), const Structure< S > &from_se, const T &from_data)
	Pass-through conversion between compatible structures.
template<typename S , typename T >
T	op_default (const Structure< S > &se, SELECTOR(T))
	Default construction of values using `Structure`.
template<typename S , typename T >
void	op_swap (const Structure< S > &se, T &v1, T &v2)
	Default swap operator.
template<typename S , typename T , typename U >
void	op_assign (const Structure< S > &s, T &dst, const U &src)
	Assignement operator between two implementations of a Structure<S>.
template<typename S , typename T , typename U >
void	op_assign (const Structure< S > &s1, const Structure< S > &s2, T &dst, const U &src)
	Assignement operator between two implementations of two differents structures.
template<typename S , typename T , typename U >
void	op_in_add (const Structure< S > &s1, const Structure< S > &s2, T &dst, const U &arg)
	Addition in place operator between two different elements.
template<typename S , typename T , typename U >
void	op_in_sub (const Structure< S > &s1, const Structure< S > &s2, T &dst, const U &arg)
	Substraction in place operator between two different elements.
template<typename S , typename T , typename U >
void	op_in_mul (const Structure< S > &s1, const Structure< S > &s2, T &dst, const U &arg)
	Multiplication in place operator between two different elements.
template<typename S , typename T , typename U >
void	op_in_div (const Structure< S > &s1, const Structure< S > &s2, T &dst, const U &arg)
	Division in place operator between two different elements.
template<typename S , typename T , typename U >
void	op_in_mod (const Structure< S > &s1, const Structure< S > &s2, T &dst, const U &arg)
	Modulo in place operator between two different elements.
template<typename S , typename T , typename U >
T	op_add (const Structure< S > &s1, const Structure< S > &s2, const T &v1, const U &v2)
	Addition operator between two different elements.
template<typename S , typename T , typename U >
T	op_sub (const Structure< S > &s1, const Structure< S > &s2, const T &v1, const U &v2)
	Substraction operator between two different elements.
template<typename S , typename T , typename U >
T	op_mul (const Structure< S > &s1, const Structure< S > &s2, const T &v1, const U &v2)
	Multiplication operator between two different elements.
template<typename S , typename T , typename U >
T	op_div (const Structure< S > &s1, const Structure< S > &s2, const T &v1, const U &v2)
	Division operator between two different elements.
template<typename S , typename T , typename U >
T	op_mod (const Structure< S > &s1, const Structure< S > &s2, const T &v1, const U &v2)
	Modulo operator between two different elements.
template<typename S , typename St , typename T >
St &	op_rin (const Structure< S > &s, St &st, const T &v)
	Input stream operator.
template<typename S , typename St , typename T >
St &	op_rout (const Structure< S > &s, St &st, const T &v)
	Output stream operator.
template<typename S1 , typename T1 , typename S2 , typename T2 >
static bool	operator< (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Comparison between Element instances.
template<typename S1 , typename T1 , typename S2 , typename T2 >
static bool	operator> (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Comparison between Element instances.
template<typename S1 , typename T1 , typename S2 , typename T2 >
static bool	operator<= (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Comparison between Element instances.
template<typename S1 , typename T1 , typename S2 , typename T2 >
static bool	operator>= (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Comparison between Element instances.
template<typename S , typename T , typename U >
static bool	operator< (const vcsn::Element< S, T > &e, const U &v)
	Comparison between Element and foreign values (left version).
template<typename S , typename T , typename U >
static bool	operator> (const vcsn::Element< S, T > &e, const U &v)
	Comparison between Element and foreign values (left version).
template<typename S , typename T , typename U >
static bool	operator>= (const vcsn::Element< S, T > &e, const U &v)
	Comparison between Element and foreign values (left version).
template<typename S , typename T , typename U >
static bool	operator<= (const vcsn::Element< S, T > &e, const U &v)
	Comparison between Element and foreign values (left version).
template<typename U , typename S , typename T >
static bool	operator< (const U &v, const vcsn::Element< S, T > &e)
	Comparison between Element and foreign values (right version).
template<typename U , typename S , typename T >
static bool	operator> (const U &v, const vcsn::Element< S, T > &e)
	Comparison between Element and foreign values (right version).
template<typename U , typename S , typename T >
static bool	operator>= (const U &v, const vcsn::Element< S, T > &e)
	Comparison between Element and foreign values (right version).
template<typename U , typename S , typename T >
static bool	operator<= (const U &v, const vcsn::Element< S, T > &e)
	Comparison between Element and foreign values (right version).
template<typename S1 , typename T1 , typename S2 , typename T2 >
static bool	operator== (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Equality between Element instances.
template<typename S , typename T , typename U >
static bool	operator== (const vcsn::Element< S, T > &e, const U &v)
	Equality between Element and foreign values (left version).
template<typename U , typename S , typename T >
static bool	operator== (const U &v, const vcsn::Element< S, T > &e)
	Equality between Element and foreign values (right version).
template<typename S1 , typename T1 , typename S2 , typename T2 >
static bool	operator!= (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Difference between Element instances.
template<typename S , typename T , typename U >
static bool	operator!= (const vcsn::Element< S, T > &e, const U &v)
	Difference between Element and foreign values (left version).
template<typename U , typename S , typename T >
static bool	operator!= (const U &v, const vcsn::Element< S, T > &e)
	Difference between Element and foreign values (right version).
template<typename S1 , typename T1 , typename S2 , typename T2 >
static vcsn::op_add_traits< S1, S2, T1, T2 >::ret_t	operator+ (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Addition between Element instances.
template<typename S , typename T , typename U >
static vcsn::Element< S, T >	operator+ (const vcsn::Element< S, T > &e, const U &v)
	Addition between Element and foreign values (left).
template<typename U , typename S , typename T >
static vcsn::Element< S, T >	operator+ (const U &v, const vcsn::Element< S, T > &e)
	Addition between Element and foreign values (right).
template<typename S1 , typename T1 , typename S2 , typename T2 >
static vcsn::op_sub_traits< S1, S2, T1, T2 >::ret_t	operator- (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Substraction between Element instances.
template<typename S , typename T , typename U >
static vcsn::Element< S, T >	operator- (const vcsn::Element< S, T > &e, const U &v)
	Substraction between Element and foreign values (left).
template<typename U , typename S , typename T >
static vcsn::Element< S, T >	operator- (const U &v, const vcsn::Element< S, T > &e)
	Substraction between Element and foreign values (right).
template<typename S1 , typename T1 , typename S2 , typename T2 >
static vcsn::op_mul_traits< S1, S2, T1, T2 >::ret_t	operator* (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Multiplication between Element instances.
template<typename S , typename T , typename U >
static vcsn::Element< S, T >	operator* (const vcsn::Element< S, T > &e, const U &v)
	Multiplication between Element and foreign values (left).
template<typename U , typename S , typename T >
static vcsn::Element< S, T >	operator* (const U &v, const vcsn::Element< S, T > &e)
	Multiplication between Element and foreign values (right).
template<typename S1 , typename T1 , typename S2 , typename T2 >
static vcsn::op_div_traits< S1, S2, T1, T2 >::ret_t	operator/ (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Division between Element instances.
template<typename S , typename T , typename U >
static vcsn::Element< S, T >	operator/ (const vcsn::Element< S, T > &e, const U &v)
	Division between Element and foreign values (left).
template<typename U , typename S , typename T >
static vcsn::Element< S, T >	operator/ (const U &v, const vcsn::Element< S, T > &e)
	Division between Element and foreign values (right).
template<typename S1 , typename T1 , typename S2 , typename T2 >
static vcsn::op_mod_traits< S1, S2, T1, T2 >::ret_t	operator% (const vcsn::Element< S1, T1 > &e1, const vcsn::Element< S2, T2 > &e2)
	Modulus between Element instances.
template<typename S , typename T , typename U >
static vcsn::Element< S, T >	operator% (const vcsn::Element< S, T > &e, const U &v)
	Modulus between Element and foreign values (left).
template<typename U , typename S , typename T >
static vcsn::Element< S, T >	operator% (const U &v, const vcsn::Element< S, T > &e)
	Modulus between Element and foreign values (right.
template<typename S , typename T >
static vcsn::Element< S, T >	operator- (const vcsn::Element< S, T > &)
	Unary negation of Element instances.
template<typename St , typename S , typename T >
static St &	operator<< (St &s, const vcsn::Element< S, T > &e)
	Output to stream.
template<typename St , typename S , typename T >
static St &	operator>> (St &s, const vcsn::Element< S, T > &e)
	Input from stream.
Determinization algorithms

template<typename A , typename AI >
Element< A, AI >	determinize (const Element< A, AI > &a)
	Build a deterministic automaton from a Boolean automaton.
template<typename A , typename AI >
Element< A, AI >	determinize (const Element< A, AI > &a, std::map< typename Element< A, AI >::hstate_t, std::set< typename Element< A, AI >::hstate_t > > &m)
	Build a deterministic automaton from a Boolean automaton, keeping trace of state-to-states correspondences.
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)
Infiltration algorithm
Returns a fresh automaton that is the infiltration of the two input ones. Precondition: The two input automata must be realtime.
template<typename A , typename T , typename U >
Element< A, T >	infiltration (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 >	infiltration (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)
Letter-to-letter FMP automaton to pair letter automaton algorithm.
Compute the pair letter automaton associated to an ltl FMP automaton.
template<typename S , typename T >
void	ltl_to_pair (const Element< S, T > &ltl, typename mute_ltl_to_pair< S, T >::ret &res)
template<typename S , typename T >
mute_ltl_to_pair< S, T >::ret	ltl_to_pair (const Element< S, T > &ltl)
Pair letter automaton to FMP transducer algorithm.
Compute the FMP transducer associated to a pair letter automaton.
template<typename S , typename T >
void	pair_to_fmp (const Element< S, T > &aut, typename mute_pair_to_fmp< S, T >::ret &res)
template<typename S , typename T >
mute_pair_to_fmp< S, T >::ret	pair_to_fmp (const Element< S, T > &aut)
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.
Shuffle algorithm
Returns a fresh automaton that is the shuffle of the two input ones. Precondition: The two input automata must be realtime.
template<typename A , typename T , typename U >
Element< A, T >	shuffle (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 >	shuffle (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)
Universal algorithm

template<typename A , typename AI >
Element< A, AI >	universal (const Element< A, AI > &a)
	Build a universal automaton from a Boolean automaton.
Default operation on automata.

template<typename S , typename R , typename T >
R	op_convert (const AutomataBase< S > &se, SELECTOR(R), const T &data)
	Default conversion between value types with computation.
template<typename S , typename T >
const T &	op_convert (const AutomataBase< S > &, SELECTOR(T), const T &from_data)
	Default conversion between value types with computation.
template<typename S , typename T , typename U >
void	op_assign (const AutomataBase< S > &s, T &dst, const U &src)
	Assignement operator between two implementations of a Structure<S>.
template<typename S , typename T >
void	op_assign (const AutomataBase< S > &concept, T &dst, const T &src)
	Default conversion between value types with computation.
template<class S , class T >
const automaton_traits< T > ::tag_t &	op_get_tag (const AutomataBase< S > &, const T &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T >::tag_t &	op_get_tag (const AutomataBase< S > &, T &)
	Default conversion between value types with computation.
template<class S , class T >
const automaton_traits< T > ::geometry_t &	op_get_geometry (const AutomataBase< S > &, const T &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T >::geometry_t &	op_get_geometry (const AutomataBase< S > &, T &)
	Default conversion between value types with computation.
template<class S , class T >
bool	op_exists (const AutomataBase< S > &s, const T &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T >::states_t	op_states (const AutomataBase< S > &, const T &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T >::hstate_t	op_get_state (const AutomataBase< S > &, const T &, int state)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::transitions_t	op_transitions (const AutomataBase< S > &, const T &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::initial_support_t	op_initial (const AutomataBase< S > &, const T &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::final_support_t	op_final (const AutomataBase< S > &, const T &)
	Default conversion between value types with computation.
template<class S , class T >
void	op_set_initial (const AutomataBase< S > &, T &, const typename automaton_traits< T >::hstate_t &state, const typename Element< S, T >::series_set_elt_t &s)
	Default conversion between value types with computation.
template<class S , class T >
Element< S, T >::series_set_elt_t	op_get_initial (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::hstate_t &state)
	Default conversion between value types with computation.
template<class S , class T >
bool	op_is_initial (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::hstate_t &state)
	Default conversion between value types with computation.
template<class S , class T >
void	op_set_final (const AutomataBase< S > &, T &, const typename automaton_traits< T >::hstate_t &state, const typename Element< S, T >::series_set_elt_t &s)
	Default conversion between value types with computation.
template<class S , class T >
Element< S, T >::series_set_elt_t	op_get_final (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::hstate_t &state)
	Default conversion between value types with computation.
template<class S , class T >
bool	op_is_final (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::hstate_t &state)
	Default conversion between value types with computation.
template<class S , class T >
void	op_set_initial (const AutomataBase< S > &, T &, int state, const typename Element< S, T >::series_set_elt_t &s)
	Default conversion between value types with computation.
template<class S , class T >
Element< S, T >::series_set_elt_t	op_get_initial (const AutomataBase< S > &, const T &, int state)
	Default conversion between value types with computation.
template<class S , class T >
bool	op_is_initial (const AutomataBase< S > &, const T &, int state)
	Default conversion between value types with computation.
template<class S , class T >
void	op_set_final (const AutomataBase< S > &, T &, int state, const typename Element< S, T >::series_set_elt_t &s)
	Default conversion between value types with computation.
template<class S , class T >
Element< S, T >::series_set_elt_t	op_get_final (const AutomataBase< S > &, const T &, int state)
	Default conversion between value types with computation.
template<class S , class T >
bool	op_is_final (const AutomataBase< S > &, const T &, int state)
	Default conversion between value types with computation.
template<class S , class T >
void	op_clear_initial (const AutomataBase< S > &, T &)
	Default conversion between value types with computation.
template<class S , class T >
void	op_clear_final (const AutomataBase< S > &, T &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T >::hstate_t	op_add_state (const AutomataBase< S > &, T &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T >::hstate_t	op_choose_state (const AutomataBase< S > &, T &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::htransition_t	op_add_transition (const AutomataBase< S > &, T &, const typename automaton_traits< T >::hstate_t &from, const typename automaton_traits< T >::hstate_t &to, const typename Element< S, T >::label_t &label)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::htransition_t	op_add_weighted_transition (const AutomataBase< S > &, T &, const typename automaton_traits< T >::hstate_t &from, const typename automaton_traits< T >::hstate_t &to, const typename Element< S, T >::semiring_elt_t &w, const typename Element< S, T >::monoid_elt_value_t &m)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::htransition_t	op_add_series_transition (const AutomataBase< S > &, T &, const typename automaton_traits< T >::hstate_t &from, const typename automaton_traits< T >::hstate_t &to, const typename Element< S, T >::series_set_elt_t &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::htransition_t	op_add_spontaneous (const AutomataBase< S > &, T &, const typename automaton_traits< T >::hstate_t &from, const typename automaton_traits< T >::hstate_t &to, const typename Element< S, T >::semiring_elt_t &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::htransition_t	op_add_letter_transition (const AutomataBase< S > &, T &, const typename automaton_traits< T >::hstate_t &from, const typename automaton_traits< T >::hstate_t &to, const typename Element< S, T >::letter_t &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::htransition_t	op_add_transition (const AutomataBase< S > &, T &, int from, int to, const typename Element< S, T >::label_t &label)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::htransition_t	op_add_weighted_transition (const AutomataBase< S > &, T &, int from, int to, const typename Element< S, T >::semiring_elt_t &w, const typename Element< S, T >::monoid_elt_value_t &m)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::htransition_t	op_add_series_transition (const AutomataBase< S > &, T &, int from, int to, const typename Element< S, T >::series_set_elt_t &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::htransition_t	op_add_spontaneous (const AutomataBase< S > &, T &, int from, int to, const typename Element< S, T >::semiring_elt_t &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T > ::htransition_t	op_add_letter_transition (const AutomataBase< S > &, T &, int from, int to, const typename Element< S, T >::letter_t &)
	Default conversion between value types with computation.
template<class S , class T >
void	op_update (const AutomataBase< S > &, T &, const typename automaton_traits< T >::htransition_t &, const typename Element< S, T >::label_t &l)
	Default conversion between value types with computation.
template<class S , class T >
void	op_del_state (const AutomataBase< S > &, T &, const typename automaton_traits< T >::hstate_t &)
	Default conversion between value types with computation.
template<class S , class T >
void	op_del_state (const AutomataBase< S > &, T &, int)
	Default conversion between value types with computation.
template<class S , class T >
void	op_del_transition (const AutomataBase< S > &, T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
bool	op_has_state (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::hstate_t &)
	Default conversion between value types with computation.
template<class S , class T >
bool	op_has_state (const AutomataBase< S > &, const T &, int)
	Default conversion between value types with computation.
template<class S , class T >
bool	op_has_transition (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T >::hstate_t	op_src_of (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
automaton_traits< T >::hstate_t	op_dst_of (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
Element< S, T >::label_t	op_label_of (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
const Element< S, T > ::series_set_elt_t	op_series_of (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
Element< S, T > ::series_set_elt_value_t	op_series_value_of (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
Element< S, T >::monoid_elt_t	op_word_of (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
Element< S, T >::semiring_elt_t	op_weight_of (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
Element< S, T >::monoid_elt_value_t	op_word_value_of (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
Element< S, T >::letter_t	op_letter_of (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.
template<class S , class T >
bool	op_is_spontaneous (const AutomataBase< S > &, const T &, const typename automaton_traits< T >::htransition_t &)
	Default conversion between value types with computation.


template<class S , class T >
Element< S, TransposeView< T > >	transpose_view (Element< S, T > &)
	This function creates a transposed view of an automaton.
template<class S , class T >
const Element< S, TransposeView< T > >	transpose_view (const Element< S, T > &)
	This function creates a transposed view of an automaton.


template<class S , class T >
automaton_traits < TransposeView< T > >::initial_support_t	op_initial (const AutomataBase< S > &, const TransposeView< T > &)
	Operations on automata implemented with TransposeView.
template<class S , class T >
automaton_traits < TransposeView< T > >::final_support_t	op_final (const AutomataBase< S > &, const TransposeView< T > &)
	Operations on automata implemented with TransposeView.
template<class S , class T >
void	op_set_initial (const AutomataBase< S > &, TransposeView< T > &, const typename automaton_traits< T >::hstate_t &state, const typename Element< S, TransposeView< T > >::series_set_elt_t &s)
	Operations on automata implemented with TransposeView.
template<class S , class T >
Element< S, TransposeView< T > >::series_set_elt_t	op_get_initial (const AutomataBase< S > &, const TransposeView< T > &, const typename automaton_traits< T >::hstate_t &)
	Operations on automata implemented with TransposeView.
template<class S , class T >
void	op_set_final (const AutomataBase< S > &, TransposeView< T > &, const typename automaton_traits< T >::hstate_t &state, const typename Element< S, T >::series_set_elt_t &s)
	Operations on automata implemented with TransposeView.
template<class S , class T >
Element< S, T >::series_set_elt_t	op_get_final (const AutomataBase< S > &, const TransposeView< T > &, const typename automaton_traits< T >::hstate_t &state)
	Operations on automata implemented with TransposeView.
template<class S , class T >
void	op_clear_initial (const AutomataBase< S > &, TransposeView< T > &)
	Operations on automata implemented with TransposeView.
template<class S , class T >
void	op_clear_final (const AutomataBase< S > &, TransposeView< T > &)
	Operations on automata implemented with TransposeView.
template<class S , class T >
automaton_traits< T >::hstate_t	op_src_of (const AutomataBase< S > &, const TransposeView< T > &, const typename automaton_traits< T >::htransition_t &)
	Operations on automata implemented with TransposeView.
template<class S , class T >
automaton_traits< T >::hstate_t	op_dst_of (const AutomataBase< S > &, const TransposeView< T > &, const typename automaton_traits< T >::htransition_t &)
	Operations on automata implemented with TransposeView.
Inequality operator for Structures.
Calls equality operator of sub-class.
template<typename S >
bool	operator!= (const vcsn::Structure< S > &a, const vcsn::Structure< S > &b)

Detailed Description

The main namespace of the Vaucanson library.

Enumeration Type Documentation

enum op_choose_max_word_length_t

Maximum length of words generated by op_choose.

To retrieve this information, just use the value named with op_choose_max_word_length.

Definition at line 130 of file free_monoid.hh.

Function Documentation

linearize_element<S, T>::alphabet_t vcsn::linearized_alphabet ( const Element< S, T > & exp )

Computes a linearized alphabet from a rational expression.

This function returns a linearized alphabet corresponding to a rational expression, with an extra zero-letter in it.

Parameters:

exp

The expression to work on.

Author:: Loic Fosse <loic@lrde.epita.fr>

See also:: linearize()

Definition at line 49 of file berry_sethi.hxx.

References linearize().

Exp vcsn::linear_exp_continuation	(	const Exp &	exp,
		const Letter &	l
	)

This function computes a continuation on linearized expressions.

This include the case when letter is zero.

Parameters:

	exp	The expression to work on.
	l	The letter used to compute the derivation.

Author:: Loic Fosse <loic@lrde.epita.fr>

Definition at line 71 of file berry_sethi.hxx.

References derivate(), and SELECT.

Referenced by BerrySethiAlgo< T_auto, S, T >::delta(), and BerrySethiAlgo< T_auto, S, T >::is_final().

bool is_cut_up ( const Element< A, AI > & a )

Check if labels are series with one element.

a Input automaton.
Returns:
is cut-up.

Definition at line 37 of file cut_up.hxx.

Element< A, AI > cut_up ( const Element< A, AI > & a )

Transform an automaton labeled with series to an automaton where all labels are series with one and only one element.

Note:: No cut-up work is done on input and output transitions.

Works on all automata and transducers labeled with polynomial series, and on automata labeled with rational series.

a Input automaton.
Returns:
Output automaton.

Definition at line 160 of file cut_up.hxx.

References Element< S, T >::structure().

Referenced by cut_up_here().

void cut_up	(	const Element< A, AI > &	a,
		Element< A, AI > &	res
	)

Transform an automaton labeled with series to an automaton where all labels are series with one and only one element.

Note:: No cut-up work is done on input and output transitions.

Works on all automata and transducers labeled with polynomial series, and on automata labeled with rational series.

a Input automaton.
res Output automaton.

Definition at line 150 of file cut_up.hxx.

References SELECT, and Element< S, T >::structure().

void cut_up_here ( Element< A, AI > & a )

Transform an automaton labeled with series to an automaton where all labels are series with one and only one element.

Note:: No cut-up work is done on input and output transitions.

Works on all automata and transducers labeled with polynomial series, and on automata labeled with rational series.

a Input automaton.

Definition at line 170 of file cut_up.hxx.

References cut_up().

output_projection_helper< S, T >::ret image ( const Element< S, T > & src )

Definition at line 290 of file image.hxx.

References Element< S, T >::structure().

bool has_successors	(	const Element< A, T > &	a,
		const typename automaton_traits< T >::hstate_t	s
	)

Whether a state has successors.

Parameters:

	a	Automaton.
	s	State.

Returns:: True is the state s has successors.

Definition at line 26 of file has_neighbour.hxx.

References Element< S, T >::value().

bool has_predecessors	(	const Element< A, T > &	a,
		const typename automaton_traits< T >::hstate_t	s
	)

Whether a state has predecessors.

Parameters:

	a	Automaton.
	s	State.

Returns:: True is the state s has predecessors.

Definition at line 37 of file has_neighbour.hxx.

References Element< S, T >::value().

void vcsn::invert	(	const Element< A, T > &	t,
		Element< A, T > &	res
	)

Invert a transducer.

Parameters:

	t	Input transducer.
	res	Inverse transducer.

Element<A, T>& vcsn::invert ( const Element< A, T > & t )

Invert a transducer.

Parameters:

t

Input transducer.

Returns:: Inverse transducer.

void vcsn::do_compose	(	const AutomataBase< S > &	,
		const algebra::FreeMonoidProduct< M1, M2 > &	,
		const lhs_t &	lhs,
		const rhs_t &	rhs,
		res_t &	ret
	)

Ambiguous composition.

Works only for boolean transducers.

Definition at line 337 of file normalized_composition.hxx.

References compose(), and eps_removal_here().

void vcsn::do_u_compose	(	const AutomataBase< S > &	,
		const algebra::FreeMonoidProduct< M1, M2 > &	,
		const lhs_t &	lhs,
		const rhs_t &	rhs,
		res_t &	ret
	)

Unambiguous composition.

Works with all type of weighted transducers.

Definition at line 360 of file normalized_composition.hxx.

References compose(), eps_removal_here(), sub_automaton_here(), and useful_states().

Referenced by u_compose().

Element< A, AI > reduce	(	const Element< A, AI > &	a,
		misc::direction_type	dir = `misc::right_left`
	)

Reduce of an automaton (default right_left).

This algorithm computes the reduce representation of an automaton with weights in a division ring.

A technical report about this algorithm is available here : http://www.lrde.epita.fr/cgi-bin/twiki/view/Publications/200901-Seminar-Delmon Proof and explanations are also available in ETA Chapter 3, Sec 4.3

Parameters:

	a	The weighted automaton to reduce.
	dir	The order in which reductions are computed.

Precondition:: The automaton a must be realtime.; The weights of the automaton a must be defined in a division ring.

See also:: semi_reduce()

Author:: Vivien Delmon, Sylvain Lombardy

Definition at line 302 of file reduce.hxx.

References is_realtime(), Element< S, T >::structure(), transpose(), and transpose_view().

Element< A, AI > semi_reduce ( const Element< A, AI > & a )

Semi reduction of an automaton.

This algorithm computes the (left) semi reduction of an automaton with weights in a division ring.

A technical report about this algorithm is available here : http://www.lrde.epita.fr/cgi-bin/twiki/view/Publications/200901-Seminar-Delmon Proof and explanations are also available in ETA Chapter 3, Sec 4.3

Parameters:

	a	The weighted automaton to reduce.
	dir	The order in which reductions are computed.

Precondition:: The automaton a must be realtime.; The weights of the automaton a must be defined in a division ring.

See also:: reduce()

Author:: Vivien Delmon, Sylvain Lombardy

Definition at line 292 of file reduce.hxx.

References is_realtime(), and Element< S, T >::structure().

void auto_translate_transitions	(	lhs_t &	dst,
		const rhs_t &	from,
		const F &	translate_fun
	)

Bug:: Write documentation and tests.

Definition at line 27 of file translate.hxx.

Element< S, TransposeView< T > > transpose_view ( Element< S, T > & a )

This function creates a transposed view of an automaton.

See also:: transpose(), TransposeView

Definition at line 48 of file transpose_view.hxx.

References Element< S, T >::structure(), and Element< S, T >::value().

Referenced by reduce(), and transpose().

const Element< S, TransposeView< T > > transpose_view ( const Element< S, T > & a )

This function creates a transposed view of an automaton.

See also:: transpose(), TransposeView

Definition at line 56 of file transpose_view.hxx.

References Element< S, T >::structure(), and Element< S, T >::value().

automaton_traits< TransposeView< T > >::initial_support_t op_initial	(	const AutomataBase< S > &	s,
		const TransposeView< T > &	v
	)