spot
2.4.3
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Classes | |
class | spot::couvreur99_check |
An implementation of the Couvreur99 emptiness-check algorithm. More... | |
class | spot::couvreur99_check_shy |
A version of spot::couvreur99_check that tries to visit known states first. More... | |
Functions | |
emptiness_check_ptr | spot::couvreur99 (const const_twa_ptr &a, option_map options=option_map()) |
Check whether the language of an automate is empty. More... | |
emptiness_check_ptr | spot::explicit_gv04_check (const const_twa_ptr &a, option_map o=option_map()) |
Emptiness check based on Geldenhuys and Valmari's TACAS'04 paper. More... | |
emptiness_check_ptr | spot::explicit_magic_search (const const_twa_ptr &a, option_map o=option_map()) |
Returns an emptiness checker on the spot::tgba automaton a. More... | |
emptiness_check_ptr | spot::bit_state_hashing_magic_search (const const_twa_ptr &a, size_t size, option_map o=option_map()) |
Returns an emptiness checker on the spot::tgba automaton a. More... | |
emptiness_check_ptr | spot::magic_search (const const_twa_ptr &a, option_map o=option_map()) |
Wrapper for the two magic_search implementations. More... | |
emptiness_check_ptr | spot::explicit_se05_search (const const_twa_ptr &a, option_map o=option_map()) |
Returns an emptiness check on the spot::tgba automaton a. More... | |
emptiness_check_ptr | spot::bit_state_hashing_se05_search (const const_twa_ptr &a, size_t size, option_map o=option_map()) |
Returns an emptiness checker on the spot::tgba automaton a. More... | |
emptiness_check_ptr | spot::se05 (const const_twa_ptr &a, option_map o) |
Wrapper for the two se05 implementations. More... | |
emptiness_check_ptr | spot::explicit_tau03_search (const const_twa_ptr &a, option_map o=option_map()) |
Returns an emptiness checker on the spot::tgba automaton a. More... | |
emptiness_check_ptr | spot::explicit_tau03_opt_search (const const_twa_ptr &a, option_map o=option_map()) |
Returns an emptiness checker on the spot::tgba automaton a. More... | |
emptiness_check_ptr spot::bit_state_hashing_magic_search | ( | const const_twa_ptr & | a, |
size_t | size, | ||
option_map | o = option_map() |
||
) |
#include <spot/twaalgos/magic.hh>
Returns an emptiness checker on the spot::tgba automaton a.
During the visit of a, the returned checker does not store explicitely the traversed states but uses the bit-state hashing technic presented in:
@book{Holzmann91, author = {G.J. Holzmann}, title = {Design and Validation of Computer Protocols}, publisher = {Prentice-Hall}, address = {Englewood Cliffs, New Jersey}, year = {1991} }
Consequently, the detection of an acceptence cycle is not ensured.
The size of the heap is limited to
size bytes.
The implemented algorithm is the same as the one of spot::explicit_magic_search.
emptiness_check_ptr spot::bit_state_hashing_se05_search | ( | const const_twa_ptr & | a, |
size_t | size, | ||
option_map | o = option_map() |
||
) |
#include <spot/twaalgos/se05.hh>
Returns an emptiness checker on the spot::tgba automaton a.
During the visit of a, the returned checker does not store explicitely the traversed states but uses the bit-state hashing technic presented in:
@book{Holzmann91, author = {G.J. Holzmann}, title = {Design and Validation of Computer Protocols}, publisher = {Prentice-Hall}, address = {Englewood Cliffs, New Jersey}, year = {1991} }
Consequently, the detection of an acceptence cycle is not ensured.
The size of the heap is limited to
size bytes.
The implemented algorithm is the same as the one of spot::explicit_se05_search.
emptiness_check_ptr spot::couvreur99 | ( | const const_twa_ptr & | a, |
option_map | options = option_map() |
||
) |
#include <spot/twaalgos/gtec/gtec.hh>
Check whether the language of an automate is empty.
This is based on the following paper.
@InProceedings{couvreur.99.fm, author = {Jean-Michel Couvreur}, title = {On-the-fly Verification of Temporal Logic}, pages = {253--271}, editor = {Jeannette M. Wing and Jim Woodcock and Jim Davies}, booktitle = {Proceedings of the World Congress on Formal Methods in the Development of Computing Systems (FM'99)}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, volume = {1708}, year = {1999}, address = {Toulouse, France}, month = {September}, isbn = {3-540-66587-0} }
A recursive definition of the algorithm would look as follows, but the implementation is of course not recursive. (<Sigma, Q, delta, q, F>
is the automaton to check, H is an associative array mapping each state to its positive DFS order or 0 if it is dead, SCC is and ACC are two stacks.)
check(<Sigma, Q, delta, q, F>, H, SCC, ACC) if q is not in H // new state H[q] = H.size + 1 SCC.push(<H[q], {}>) forall <a, s> : <q, _, a, s> in delta ACC.push(a) res = check(<Sigma, Q, delta, s, F>, H, SCC, ACC) if res return res <n, _> = SCC.top() if n = H[q] SCC.pop() mark_reachable_states_as_dead(<Sigma, Q, delta, q, F>, H$) return 0 else if H[q] = 0 // dead state ACC.pop() return true else // state in stack: merge SCC all = {} do <n, a> = SCC.pop() all = all union a union { ACC.pop() } until n <= H[q] SCC.push(<n, all>) if all != F return 0 return new emptiness_check_result(necessary data)
check() returns 0 iff the automaton's language is empty. It returns an instance of emptiness_check_result. If the automaton accept a word. (Use emptiness_check_result::accepting_run() to extract an accepting run.)
There are two variants of this algorithm: spot::couvreur99_check and spot::couvreur99_check_shy. They differ in their memory usage, the number for successors computed before they are used and the way the depth first search is directed.
spot::couvreur99_check performs a straightforward depth first search. The DFS stacks store twa_succ_iterators, so that only the iterators which really are explored are computed.
spot::couvreur99_check_shy tries to explore successors which are visited states first. this helps to merge SCCs and generally helps to produce shorter counter-examples. However this algorithm cannot stores unprocessed successors as twa_succ_iterators: it must compute all successors of a state at once in order to decide which to explore first, and must keep a list of all unexplored successors in its DFS stack.
The couvreur99() function is a wrapper around these two flavors of the algorithm. options is an option map that specifies which algorithms should be used, and how.
The following options are available.
"shy"
: if non zero, then spot::couvreur99_check_shy is used, otherwise (and by default) spot::couvreur99_check is used."poprem"
: specifies how the algorithm should handle the destruction of non-accepting maximal strongly connected components. If poprem
is non null, the algorithm will keep a list of all states of a SCC that are fully processed and should be removed once the MSCC is popped. If poprem
is null (the default), the MSCC will be traversed again (i.e. generating the successors of the root recursively) for deletion. This is a choice between memory and speed."group"
: this options is used only by spot::couvreur99_check_shy. If non null (the default), the successors of all the states that belong to the same SCC will be considered when choosing a successor. Otherwise, only the successor of the topmost state on the DFS stack are considered. emptiness_check_ptr spot::explicit_gv04_check | ( | const const_twa_ptr & | a, |
option_map | o = option_map() |
||
) |
#include <spot/twaalgos/gv04.hh>
Emptiness check based on Geldenhuys and Valmari's TACAS'04 paper.
The original algorithm, coming from the following paper, has only been slightly modified to work on transition-based automata.
@InProceedings{geldenhuys.04.tacas, author = {Jaco Geldenhuys and Antti Valmari}, title = {Tarjan's Algorithm Makes On-the-Fly {LTL} Verification More Efficient}, booktitle = {Proceedings of the 10th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS'04)}, editor = {Kurt Jensen and Andreas Podelski}, pages = {205--219}, year = {2004}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, volume = {2988}, isbn = {3-540-21299-X} }
emptiness_check_ptr spot::explicit_magic_search | ( | const const_twa_ptr & | a, |
option_map | o = option_map() |
||
) |
#include <spot/twaalgos/magic.hh>
Returns an emptiness checker on the spot::tgba automaton a.
During the visit of a, the returned checker stores explicitely all the traversed states. The method check() of the checker can be called several times (until it returns a null pointer) to enumerate all the visited acceptance paths. The implemented algorithm is the following:
procedure check () begin call dfs_blue(s0); end; procedure dfs_blue (s) begin s.color = blue; for all t in post(s) do if t.color == white then call dfs_blue(t); end if; if (the edge (s,t) is accepting) then target = s; call dfs_red(t); end if; end for; end; procedure dfs_red(s) begin s.color = red; if s == target then report cycle end if; for all t in post(s) do if t.color == blue then call dfs_red(t); end if; end for; end;
This algorithm is an adaptation to TBA of the one (which deals with accepting states) presented in
Article{ courcoubetis.92.fmsd, author = {Costas Courcoubetis and Moshe Y. Vardi and Pierre Wolper and Mihalis Yannakakis}, title = {Memory-Efficient Algorithm for the Verification of Temporal Properties}, journal = {Formal Methods in System Design}, pages = {275--288}, year = {1992}, volume = {1} }
godefroid.93.pstv
, not courcoubetis.92.fmsd
. emptiness_check_ptr spot::explicit_se05_search | ( | const const_twa_ptr & | a, |
option_map | o = option_map() |
||
) |
#include <spot/twaalgos/se05.hh>
Returns an emptiness check on the spot::tgba automaton a.
During the visit of a, the returned checker stores explicitely all the traversed states. The method check() of the checker can be called several times (until it returns a null pointer) to enumerate all the visited accepting paths. The implemented algorithm is an optimization of spot::explicit_magic_search and is the following:
procedure check () begin call dfs_blue(s0); end; procedure dfs_blue (s) begin s.color = cyan; for all t in post(s) do if t.color == white then call dfs_blue(t); else if t.color == cyan and (the edge (s,t) is accepting or (it exists a predecessor p of s in st_blue and s != t and the arc between p and s is accepting)) then report cycle; end if; if the edge (s,t) is accepting then call dfs_red(t); end if; end for; s.color = blue; end; procedure dfs_red(s) begin if s.color == cyan then report cycle; end if; s.color = red; for all t in post(s) do if t.color == blue then call dfs_red(t); end if; end for; end;
It is an adaptation to TBA of the one presented in
@techreport{SE04, author = {Stefan Schwoon and Javier Esparza}, institution = {Universit{\"a}t Stuttgart, Fakult\"at Informatik, Elektrotechnik und Informationstechnik}, month = {November}, number = {2004/06}, title = {A Note on On-The-Fly Verification Algorithms}, year = {2004}, url = {http://www.fmi.uni-stuttgart.de/szs/publications/info/schwoosn.SE04.shtml} }
emptiness_check_ptr spot::explicit_tau03_opt_search | ( | const const_twa_ptr & | a, |
option_map | o = option_map() |
||
) |
#include <spot/twaalgos/tau03opt.hh>
Returns an emptiness checker on the spot::tgba automaton a.
During the visit of a, the returned checker stores explicitely all the traversed states. The implemented algorithm is the following:
procedure check () begin weight = 0; // the null vector call dfs_blue(s0); end; procedure dfs_blue (s) begin s.color = cyan; s.acc = emptyset; s.weight = weight; for all t in post(s) do let (s, l, a, t) be the edge from s to t; if t.color == white then for all b in a do weight[b] = weight[b] + 1; end for; call dfs_blue(t); for all b in a do weight[b] = weight[b] - 1; end for; end if; Acc = s.acc U a; if t.color == cyan && (Acc U support(weight - t.weight) U t.acc) == all_acc then report a cycle; else if Acc not included in t.acc then t.acc := t.acc U Acc; call dfs_red(t, Acc); end if; end for; s.color = blue; end; procedure dfs_red(s, Acc) begin for all t in post(s) do let (s, l, a, t) be the edge from s to t; if t.color == cyan && (Acc U support(weight - t.weight) U t.acc) == all_acc then report a cycle; else if t.color != white and Acc not included in t.acc then t.acc := t.acc U Acc; call dfs_red(t, Acc); end if; end for; end;
This algorithm is a generalisation to TGBA of the one implemented in spot::explicit_se05_search. It is based on the acceptance set labelling of states used in spot::explicit_tau03_search. Moreover, it introduce a slight optimisation based on vectors of integers counting for each acceptance condition how many time the condition has been visited in the path stored in the blue stack. Such a vector is associated to each state of this stack.
emptiness_check_ptr spot::explicit_tau03_search | ( | const const_twa_ptr & | a, |
option_map | o = option_map() |
||
) |
#include <spot/twaalgos/tau03.hh>
Returns an emptiness checker on the spot::tgba automaton a.
During the visit of a, the returned checker stores explicitely all the traversed states. The implemented algorithm is the following:
procedure check () begin call dfs_blue(s0); end; procedure dfs_blue (s) begin s.color = blue; s.acc = emptyset; for all t in post(s) do if t.color == white then call dfs_blue(t); end if; end for; for all t in post(s) do let (s, l, a, t) be the edge from s to t; if s.acc U a not included in t.acc then call dfs_red(t, a U s.acc); end if; end for; if s.acc == all_acc then report a cycle; end if; end; procedure dfs_red(s, A) begin s.acc = s.acc U A; for all t in post(s) do if t.color != white and A not included in t.acc then call dfs_red(t, A); end if; end for; end;
This algorithm is the one presented in
@techreport{HUT-TCS-A83, address = {Espoo, Finland}, author = {Heikki Tauriainen}, institution = {Helsinki University of Technology, Laboratory for Theoretical Computer Science}, month = {December}, number = {A83}, pages = {132}, title = {On Translating Linear Temporal Logic into Alternating and Nondeterministic Automata}, type = {Research Report}, year = {2003}, url = {http://www.tcs.hut.fi/Publications/info/bibdb.HUT-TCS-A83.shtml} }
emptiness_check_ptr spot::magic_search | ( | const const_twa_ptr & | a, |
option_map | o = option_map() |
||
) |
#include <spot/twaalgos/magic.hh>
Wrapper for the two magic_search implementations.
This wrapper calls explicit_magic_search_search() or bit_state_hashing_magic_search() according to the "bsh"
option in the option_map
. If "bsh"
is set and non null, its value is used as the size of the hash map.
emptiness_check_ptr spot::se05 | ( | const const_twa_ptr & | a, |
option_map | o | ||
) |
#include <spot/twaalgos/se05.hh>
Wrapper for the two se05 implementations.
This wrapper calls explicit_se05_search() or bit_state_hashing_se05_search() according to the "bsh"
option in the option_map
. If "bsh"
is set and non null, its value is used as the size of the hash map.