spot  2.7.2
Classes | Enumerations | Functions
Miscellaneous algorithms on TωA

Classes

class  spot::scc_info_node
 Storage for SCC related information. More...
 
class  spot::scc_info
 Compute an SCC map and gather assorted information. More...
 
struct  spot::twa_statistics
 
struct  spot::twa_sub_statistics
 
class  spot::printable_formula
 
class  spot::printable_acc_cond
 
class  spot::printable_scc_info
 
class  spot::stat_printer
 prints various statistics about a TGBA More...
 

Enumerations

enum  spot::scc_info_options {
  spot::scc_info_options::NONE = 0, spot::scc_info_options::STOP_ON_ACC = 1, spot::scc_info_options::TRACK_STATES = 2, spot::scc_info_options::TRACK_SUCCS = 4,
  spot::scc_info_options::TRACK_STATES_IF_FIN_USED = 8, spot::scc_info_options::ALL = TRACK_STATES | TRACK_SUCCS
}
 Options to alter the behavior of scc_info. More...
 

Functions

bool spot::isomorphism_checker::is_isomorphic (const const_twa_graph_ptr aut)
 Check whether an automaton is isomorphic to the one passed to the constructor. More...
 
static bool spot::isomorphism_checker::are_isomorphic (const const_twa_graph_ptr ref, const const_twa_graph_ptr aut)
 Check whether two automata are isomorphic. More...
 
twa_graph_ptr spot::canonicalize (twa_graph_ptr aut)
 Reorder the states and transitions of aut in a way that will be the same for every isomorphic automata. More...
 
twa_graph_ptr spot::copy (const const_twa_ptr &aut, twa::prop_set p, bool preserve_names=false, unsigned max_states=-1U)
 Build an explicit automaton from all states of aut,. More...
 
twa_graph_ptr spot::dualize (const const_twa_graph_ptr &aut)
 Complement an automaton by dualizing it. More...
 
twa_graph_ptr spot::g_f_terminal_inplace (twa_graph_ptr f_terminal, bool state_based=false)
 Given a terminal automaton f_terminal recognizing some formula F(φ), modify it to recognize GF(φ). More...
 
unsigned spot::count_nondet_states (const const_twa_graph_ptr &aut)
 Count the number of states with non-deterministic branching in aut. More...
 
bool spot::is_universal (const const_twa_graph_ptr &aut)
 Return true iff aut is universal. More...
 
bool spot::is_deterministic (const const_twa_graph_ptr &aut)
 Return true iff aut is deterministic. More...
 
void spot::highlight_nondet_states (twa_graph_ptr &aut, unsigned color)
 Highlight nondeterministic states. More...
 
void spot::highlight_nondet_edges (twa_graph_ptr &aut, unsigned color)
 Highlight nondeterministic edges. More...
 
bool spot::is_unambiguous (const const_twa_graph_ptr &aut)
 Whether the automaton aut is unambiguous. More...
 
bool spot::check_unambiguous (const twa_graph_ptr &aut)
 Like is_unambiguous(), but also sets the property in the twa. More...
 
bool spot::scc_has_rejecting_cycle (scc_info &map, unsigned scc)
 Whether the SCC number scc in map has a rejecting cycle. More...
 
bool spot::is_inherently_weak_scc (scc_info &map, unsigned scc)
 Whether the SCC number scc in map is inherently weak. More...
 
bool spot::is_weak_scc (scc_info &map, unsigned scc)
 Whether the SCC number scc in map is weak. More...
 
bool spot::is_complete_scc (scc_info &map, unsigned scc)
 Whether the SCC number scc in map is complete. More...
 
bool spot::is_terminal_scc (scc_info &map, unsigned scc)
 Whether the SCC number scc in map is terminal. More...
 
twa_graph_ptr spot::random_graph (int n, float d, const atomic_prop_set *ap, const bdd_dict_ptr &dict, unsigned n_accs=0, float a=0.1, float t=0.5, bool deterministic=false, bool state_acc=false, bool colored=false)
 Construct a twa randomly. More...
 
twa_graph_ptr spot::split_edges (const const_twa_graph_ptr &aut)
 transform edges into transitions More...
 
twa_statistics spot::stats_reachable (const const_twa_ptr &g)
 Compute statistics for an automaton. More...
 
twa_sub_statistics spot::sub_stats_reachable (const const_twa_ptr &g)
 Compute sub statistics for an automaton. More...
 
void spot::strip_acceptance_here (twa_graph_ptr a)
 Remove all acceptance sets from a twa_graph. More...
 
twa_graph_ptr spot::tgba_powerset (const const_twa_graph_ptr &aut, power_map &pm, bool merge=true)
 Build a deterministic automaton, ignoring acceptance conditions. More...
 
twa_graph_ptr spot::tgba_powerset (const const_twa_graph_ptr &aut)
 Build a deterministic automaton, ignoring acceptance conditions. More...
 

Detailed Description

Enumeration Type Documentation

◆ scc_info_options

#include <spot/twaalgos/sccinfo.hh>

Options to alter the behavior of scc_info.

Enumerator
NONE 

Stop exploring when an accepting SCC is found, and do not track the states of each SCC.

STOP_ON_ACC 

Stop exploring after an accepting SCC has been found. Using this option forbids future uses of is_useful_scc() and is_useful_state(). Using it will also cause the output of succ() to be incomplete.

TRACK_STATES 

Keep a vector of all states belonging to each SCC. Using this option is a precondition for using states_of(), edges_of(), inner_edges_of(), states_on_acc_cycle_of(), and determine_unknown_acceptance().

TRACK_SUCCS 

Keep a list of successors of each SCCs. Using this option is a precondition for using succ(), is_useful_scc(), and is_useful_state().

TRACK_STATES_IF_FIN_USED 

Conditionally track states if the acceptance conditions uses Fin. This is sufficiant for determine_unknown_acceptance().

ALL 

Default behavior: explore everything and track states and succs.

Function Documentation

◆ are_isomorphic()

static bool spot::isomorphism_checker::are_isomorphic ( const const_twa_graph_ptr  ref,
const const_twa_graph_ptr  aut 
)
static

#include <spot/twaalgos/are_isomorphic.hh>

Check whether two automata are isomorphic.

◆ canonicalize()

twa_graph_ptr spot::canonicalize ( twa_graph_ptr  aut)

#include <spot/twaalgos/canonicalize.hh>

Reorder the states and transitions of aut in a way that will be the same for every isomorphic automata.

◆ check_unambiguous()

bool spot::check_unambiguous ( const twa_graph_ptr &  aut)

#include <spot/twaalgos/isunamb.hh>

Like is_unambiguous(), but also sets the property in the twa.

◆ copy()

twa_graph_ptr spot::copy ( const const_twa_ptr &  aut,
twa::prop_set  p,
bool  preserve_names = false,
unsigned  max_states = -1U 
)
inline

#include <spot/twaalgos/copy.hh>

Build an explicit automaton from all states of aut,.

This function was deprecated in Spot 2.4. Use the function make_twa_graph() instead.

References spot::make_twa_graph().

◆ count_nondet_states()

unsigned spot::count_nondet_states ( const const_twa_graph_ptr &  aut)

#include <spot/twaalgos/isdet.hh>

Count the number of states with non-deterministic branching in aut.

The automaton is universal if it has 0 states with non-deterministic branching but it is more efficient to call is_universal() if you do not care about the number of non-deterministic states.

◆ dualize()

twa_graph_ptr spot::dualize ( const const_twa_graph_ptr &  aut)

#include <spot/twaalgos/dualize.hh>

Complement an automaton by dualizing it.

Given an automaton aut of any type, produces the dual as output. The automaton will be completed if it isn't already. If it is deterministic and complete, complementing the automaton can be done by just complementing the acceptance condition.

In particular, this implies that an input that use generalized Büchi will be output as generalized co-Büchi.

Functions like to_generalized_buchi() or remove_fin() are frequently called on existential automata after dualize() to obtain an easier acceptance condition, but maybe at the cost of losing determinism.

If the input automaton is deterministic, the output will be deterministic. If the input automaton is existential, the output will be universal. If the input automaton is universal, the output will be existential. Finally, if the input automaton is alternating, the result is alternating. More can be found on page 22 (Definition 1.6) of:

@mastersthesis{loding.98.methodsfor
  author = {Christof Löding}
  title  = {Methods for the Transformation of ω-Automata: Complexity
           and Connection to Second Order Logic}
  school = {Institute of Computer Science and Applied Mathematics
            Christian-Albrechts-University of Kiel}
  year   = {1998}
}

◆ g_f_terminal_inplace()

twa_graph_ptr spot::g_f_terminal_inplace ( twa_graph_ptr  f_terminal,
bool  state_based = false 
)

#include <spot/twaalgos/gfguarantee.hh>

Given a terminal automaton f_terminal recognizing some formula F(φ), modify it to recognize GF(φ).

If state_based is set, the automaton all terminal states are replaced by a unique accepting state that has the same outgoing transitions as the initial state, and the initial state is actually relocated to that accepting state. The latter point is not necessary, but it favors shorter accepting cycles.

If state_based is not set, all transition going to terminal states are made accepting and redirected to the initial state.

This construction is inspired by a similar construction in the LICS'18 paper by J. Esparza, J. Křetínský, and S. Sickert.

◆ highlight_nondet_edges()

void spot::highlight_nondet_edges ( twa_graph_ptr &  aut,
unsigned  color 
)

#include <spot/twaalgos/isdet.hh>

Highlight nondeterministic edges.

An edge is nondeterministic if there exist another edge leaving the same source state, with a compatible label (i.e., the conjunction of the two labels is not false).

Parameters
autthe automaton to process
colorthe color to give to nondeterministic edges.

◆ highlight_nondet_states()

void spot::highlight_nondet_states ( twa_graph_ptr &  aut,
unsigned  color 
)

#include <spot/twaalgos/isdet.hh>

Highlight nondeterministic states.

A state is nondeterministic if it has two outgoing edges whose labels are not incompatibles.

Parameters
autthe automaton to process
colorthe color to give to nondeterministic states.

◆ is_complete_scc()

bool spot::is_complete_scc ( scc_info map,
unsigned  scc 
)

#include <spot/twaalgos/isweakscc.hh>

Whether the SCC number scc in map is complete.

An SCC is complete iff for all states and all label there exists a transition that stays into this SCC. For this function, universal transitions are considered in the SCC if all there destination are into the SCC.

◆ is_deterministic()

bool spot::is_deterministic ( const const_twa_graph_ptr &  aut)

#include <spot/twaalgos/isdet.hh>

Return true iff aut is deterministic.

An automaton is called deterministic if it is both universal and existential.

◆ is_inherently_weak_scc()

bool spot::is_inherently_weak_scc ( scc_info map,
unsigned  scc 
)

#include <spot/twaalgos/isweakscc.hh>

Whether the SCC number scc in map is inherently weak.

An SCC is inherently weak if either its cycles are all accepting, or they are all non-accepting.

Note the terminal SCCs are also inherently weak with that definition.

◆ is_isomorphic()

bool spot::isomorphism_checker::is_isomorphic ( const const_twa_graph_ptr  aut)

#include <spot/twaalgos/are_isomorphic.hh>

Check whether an automaton is isomorphic to the one passed to the constructor.

Two automata are considered isomorphic if there exists a bijection f between the states of a1 and the states of a2 such that for any pair of states (s1, s2) of a1, there is a transition from s1 to s2 with condition c and acceptance set A iff there is a transition with condition c and acceptance set A between f(s1) and f(s2) in a2. This can be done simply by checking if canonicalize(aut1) == canonicalize(aut2), but is_isomorphic can do some optimizations in some cases.

◆ is_terminal_scc()

bool spot::is_terminal_scc ( scc_info map,
unsigned  scc 
)

#include <spot/twaalgos/isweakscc.hh>

Whether the SCC number scc in map is terminal.

An SCC is terminal if it is weak, complete, and accepting.

◆ is_unambiguous()

bool spot::is_unambiguous ( const const_twa_graph_ptr &  aut)

#include <spot/twaalgos/isunamb.hh>

Whether the automaton aut is unambiguous.

An automaton is unambiguous if each accepted word is recognized by only one path.

We check unambiguousity by synchronizing the automaton with itself, and then making sure that the co-reachable part of the squared automaton has the same size as the co-reachable part of the original automaton.

◆ is_universal()

bool spot::is_universal ( const const_twa_graph_ptr &  aut)

#include <spot/twaalgos/isdet.hh>

Return true iff aut is universal.

This function is more efficient than count_nondet_states() when the automaton is nondeterministic, because it can return before the entire automaton has been explored.

In addition to returning the result as a Boolean, this will set the prop_universal() property of the automaton as a side-effect, so further calls will return in constant-time.

◆ is_weak_scc()

bool spot::is_weak_scc ( scc_info map,
unsigned  scc 
)

#include <spot/twaalgos/isweakscc.hh>

Whether the SCC number scc in map is weak.

An SCC is weak if its non-accepting, or if all its transition are fully accepting (i.e., the belong to all acceptance sets).

Note that terminal SCCs are also weak with that definition.

◆ random_graph()

twa_graph_ptr spot::random_graph ( int  n,
float  d,
const atomic_prop_set ap,
const bdd_dict_ptr &  dict,
unsigned  n_accs = 0,
float  a = 0.1,
float  t = 0.5,
bool  deterministic = false,
bool  state_acc = false,
bool  colored = false 
)

#include <spot/twaalgos/randomgraph.hh>

Construct a twa randomly.

Parameters
nThe number of states wanted in the automata (>0). All states will be connected, and there will be no dead state.
dThe density of the automata. This is the probability (between 0.0 and 1.0), to add a transition between two states. All states have at least one outgoing transition, so d is considered only when adding the remaining transition. A density of 1 means all states will be connected to each other.
apThe list of atomic property that should label the transition.
dictThe bdd_dict to used for this automata.
n_accsThe number of acceptance sets to use. If this number is non null, then there is no guarantee that the generated graph contains an accepting cycle (raise the value of a to improve the chances).
aThe probability (between 0.0 and 1.0) that a transition belongs to an acceptance set.
tThe probability (between 0.0 and 1.0) that an atomic proposition is true.
deterministicbuild a complete and deterministic automaton
state_accbuild an automaton with state-based acceptance
coloredbuild an automaton in which each transition (or state) belongs to a single acceptance set.

This algorithms is adapted from the one in Fig 6.2 page 48 of

@TechReport{          tauriainen.00.a66,
  author        = {Heikki Tauriainen},
  title   = {Automated Testing of {B\"u}chi Automata Translators for
                  {L}inear {T}emporal {L}ogic},
  address        = {Espoo, Finland},
  institution = {Helsinki University of Technology, Laboratory for
                  Theoretical Computer Science},
  number        = {A66},
  year        = {2000},
  url        = {http://citeseer.nj.nec.com/tauriainen00automated.html},
  type        = {Research Report},
  note        = {Reprint of Master's thesis}
}

Although the intent is similar, there are some differences between the above published algorithm and this implementation. First labels are on transitions, and acceptance conditions are generated too. Second, the number of successors of a node is chosen in $[1,n]$ following a normal distribution with mean $1+(n-1)d$ and variance $(n-1)d(1-d)$. (This is less accurate, but faster than considering all possible n successors one by one.)

Note that while this constructs an automaton with random acceptance sets, this does not set the acceptance condition.

◆ scc_has_rejecting_cycle()

bool spot::scc_has_rejecting_cycle ( scc_info map,
unsigned  scc 
)

#include <spot/twaalgos/isweakscc.hh>

Whether the SCC number scc in map has a rejecting cycle.

◆ split_edges()

twa_graph_ptr spot::split_edges ( const const_twa_graph_ptr &  aut)

#include <spot/twaalgos/split.hh>

transform edges into transitions

Create a new version of the automaton where all edges are split so that they are all labeled by a conjunction of all atomic propositions. After this we can consider that each edge of the automate is a transition labeled by one letter.

◆ stats_reachable()

twa_statistics spot::stats_reachable ( const const_twa_ptr &  g)

#include <spot/twaalgos/stats.hh>

Compute statistics for an automaton.

◆ strip_acceptance_here()

void spot::strip_acceptance_here ( twa_graph_ptr  a)

#include <spot/twaalgos/stripacc.hh>

Remove all acceptance sets from a twa_graph.

This will also set the acceptance condition to true, and mark the automaton as weak. Doing so obviously makes all recognized infinite runs accepting.

◆ sub_stats_reachable()

twa_sub_statistics spot::sub_stats_reachable ( const const_twa_ptr &  g)

#include <spot/twaalgos/stats.hh>

Compute sub statistics for an automaton.

◆ tgba_powerset() [1/2]

twa_graph_ptr spot::tgba_powerset ( const const_twa_graph_ptr &  aut,
power_map pm,
bool  merge = true 
)

#include <spot/twaalgos/powerset.hh>

Build a deterministic automaton, ignoring acceptance conditions.

This create a deterministic automaton that recognizes the same language as aut would if its acceptance conditions were ignored. This is the classical powerset algorithm.

If pm is supplied it will be filled with the set of original states associated to each state of the deterministic automaton. The merge argument can be set to false to prevent merging of transitions.

◆ tgba_powerset() [2/2]

twa_graph_ptr spot::tgba_powerset ( const const_twa_graph_ptr &  aut)

#include <spot/twaalgos/powerset.hh>

Build a deterministic automaton, ignoring acceptance conditions.

This create a deterministic automaton that recognizes the same language as aut would if its acceptance conditions were ignored. This is the classical powerset algorithm.

If pm is supplied it will be filled with the set of original states associated to each state of the deterministic automaton. The merge argument can be set to false to prevent merging of transitions.


Please direct any question, comment, or bug report to the Spot mailing list at spot@lrde.epita.fr.
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