BackwardBisimulation.h

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/*
 * This file is part of Algorithms library toolkit.
 * Copyright (C) 2017 Jan Travnicek (jan.travnicek@fit.cvut.cz)
 
 * Algorithms library toolkit is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 
 * Algorithms library toolkit is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 
 * You should have received a copy of the GNU General Public License
 * along with Algorithms library toolkit.  If not, see <http://www.gnu.org/licenses/>.
 */
 
#pragma once
 
#include <alib/set>
#include <alib/map>
 
#include <automaton/TA/DFTA.h>
#include <automaton/TA/NFTA.h>
 
#include <automaton/TA/UnorderedDFTA.h>
#include <automaton/TA/UnorderedNFTA.h>
 
#include <automaton/FSM/DFA.h>
#include <automaton/FSM/NFA.h>
 
#include <automaton/TA/ArcFactoredDeterministicZAutomaton.h>
#include <automaton/TA/ArcFactoredNondeterministicZAutomaton.h>
 
namespace automaton {
 
namespace properties {
 
class BackwardBisimulation {
    template < class StateType >
    static ext::set < ext::pair < StateType, StateType > > initial ( const ext::set < StateType > & states, const ext::set < StateType > & initials ) {
        ext::set < ext::pair < StateType, StateType > > init;
 
        for ( const StateType & a : states ) {
            for ( const StateType & b : states ) {
                if ( initials.count ( a ) == initials.count ( b ) ) {
                    init.insert ( ext::make_pair ( a, b ) );
                    init.insert ( ext::make_pair ( b, a ) );
                }
            }
        }
 
        return init;
    }
 
public:
    template < class SymbolType, class StateType >
    static ext::set < ext::pair < StateType, StateType > > backwardBisimulation ( const automaton::DFA < SymbolType, StateType > & fta );
 
    template < class SymbolType, class StateType >
    static ext::set < ext::pair < StateType, StateType > > backwardBisimulation ( const automaton::NFA < SymbolType, StateType > & fta );
 
    template < class SymbolType, class StateType >
    static ext::set < ext::pair < StateType, StateType > > backwardBisimulation ( const automaton::ArcFactoredDeterministicZAutomaton < SymbolType, StateType > & afdza );
 
    template < class SymbolType, class StateType >
    static ext::set < ext::pair < StateType, StateType > > backwardBisimulation ( const automaton::ArcFactoredNondeterministicZAutomaton < SymbolType, StateType > & afnza );
 
    template < class SymbolType, class StateType >
    static ext::set < ext::pair < StateType, StateType > > backwardBisimulation ( const automaton::DFTA < SymbolType, StateType > & fta );
 
    template < class SymbolType, class StateType >
    static ext::set < ext::pair < StateType, StateType > > backwardBisimulation ( const automaton::NFTA < SymbolType, StateType > & fta );
 
    template < class SymbolType, class StateType >
    static ext::set < ext::pair < StateType, StateType > > backwardBisimulation ( const automaton::UnorderedDFTA < SymbolType, StateType > & fta );
 
    template < class SymbolType, class StateType >
    static ext::set < ext::pair < StateType, StateType > > backwardBisimulation ( const automaton::UnorderedNFTA < SymbolType, StateType > & fta );
};
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > BackwardBisimulation::backwardBisimulation ( const automaton::DFA < SymbolType, StateType > & fta ) {
    return backwardBisimulation ( NFA < SymbolType, StateType > ( fta ) );
}
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > BackwardBisimulation::backwardBisimulation ( const automaton::NFA < SymbolType, StateType > & fta ) {
    ext::set < ext::pair < StateType, StateType > > backwardBisimulation = initial ( fta.getStates ( ), { fta.getInitialState ( ) } );
 
    bool changed;
    do {
        changed = false;
 
        for ( const StateType & p : fta.getStates ( ) ) {
            for ( const StateType & q : fta.getStates ( ) ) {
                if ( ! backwardBisimulation.contains ( ext::make_pair ( p, q ) ) )
                    continue;
 
                for ( const std::pair < const ext::pair < StateType, SymbolType >, StateType > & pTransition : fta.getTransitionsToState ( p ) ) {
 
                    bool exists = false;
                    for ( const std::pair < const ext::pair < StateType, SymbolType >, StateType > & qTransition : fta.getTransitionsToState ( q ) ) {
                        if ( qTransition.first.second != pTransition.first.second )
                            continue;
 
                        if ( backwardBisimulation.contains ( ext::make_pair ( pTransition.first.first, qTransition.first.first ) ) ) {
                            exists = true;
                            break;
                        }
                    }
 
                    if ( ! exists ) {
                        backwardBisimulation.erase ( ext::make_pair ( p, q ) );
                        backwardBisimulation.erase ( ext::make_pair ( q, p ) );
                        changed = true;
                        break;
                    }
                }
            }
        }
    } while ( changed );
 
    return backwardBisimulation;
}
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > BackwardBisimulation::backwardBisimulation ( const automaton::ArcFactoredDeterministicZAutomaton < SymbolType, StateType > & afdza ) {
    return backwardBisimulation ( ArcFactoredNondeterministicZAutomaton < SymbolType, StateType > ( afdza ) );
}
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > BackwardBisimulation::backwardBisimulation ( const automaton::ArcFactoredNondeterministicZAutomaton < SymbolType, StateType > & afnza ) {
    ext::set < ext::pair < StateType, StateType > > backwardBisimulation = initial ( afnza.getStates ( ), { } );
 
    bool changed;
    do {
        changed = false;
 
        for ( const StateType & p : afnza.getStates ( ) ) {
            for ( const StateType & q : afnza.getStates ( ) ) {
                if ( ! backwardBisimulation.contains ( ext::make_pair ( p, q ) ) )
                    continue;
 
                for ( const std::pair < const ext::variant < SymbolType, ext::pair < StateType, StateType > >, StateType > & pTransition : afnza.getTransitionsToState ( p ) ) {
                    if ( ! pTransition.first.template is < SymbolType > ( ) )
                        continue;
 
                    const SymbolType & pSource = pTransition.first.template get < SymbolType > ( );
 
                    bool exists = false;
                    for ( const std::pair < const ext::variant < SymbolType, ext::pair < StateType, StateType > >, StateType > & qTransition : afnza.getTransitionsToState ( q ) ) {
                        if ( ! qTransition.first.template is < SymbolType > ( ) )
                            continue;
 
                        const SymbolType & qSource = qTransition.first.template get < SymbolType > ( );
 
                        if ( qSource != pSource )
                            continue;
 
                        exists = true;
                        break;
                    }
 
                    if ( ! exists ) {
                        backwardBisimulation.erase ( ext::make_pair ( p, q ) );
                        backwardBisimulation.erase ( ext::make_pair ( q, p ) );
                        changed = true;
                        break;
                    }
                }
            }
        }
    } while ( changed );
 
    do {
        changed = false;
 
        for ( const StateType & p : afnza.getStates ( ) ) {
            for ( const StateType & q : afnza.getStates ( ) ) {
                if ( ! backwardBisimulation.contains ( ext::make_pair ( p, q ) ) )
                    continue;
 
                for ( const std::pair < const ext::variant < SymbolType, ext::pair < StateType, StateType > >, StateType > & pTransition : afnza.getTransitionsToState ( p ) ) {
                    if ( pTransition.first.template is < SymbolType > ( ) )
                        continue;
 
                    const ext::pair < StateType, StateType > & pSource = pTransition.first.template get < ext::pair < StateType, StateType > > ( );
 
                    bool exists = false;
                    for ( const std::pair < const ext::variant < SymbolType, ext::pair < StateType, StateType > >, StateType > & qTransition : afnza.getTransitionsToState ( q ) ) {
                        if ( qTransition.first.template is < SymbolType > ( ) )
                            continue;
 
                        const ext::pair < StateType, StateType > & qSource = qTransition.first.template get < ext::pair < StateType, StateType > > ( );
 
                        if ( backwardBisimulation.contains ( ext::make_pair ( pSource.first, qSource.first ) )
                          && backwardBisimulation.contains ( ext::make_pair ( pSource.second, qSource.second ) ) ) {
                            exists = true;
                            break;
                        }
                    }
 
                    if ( ! exists ) {
                        backwardBisimulation.erase ( ext::make_pair ( p, q ) );
                        backwardBisimulation.erase ( ext::make_pair ( q, p ) );
                        changed = true;
                        break;
                    }
                }
            }
        }
    } while ( changed );
 
    return backwardBisimulation;
}
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > BackwardBisimulation::backwardBisimulation ( const automaton::DFTA < SymbolType, StateType > & fta ) {
    return backwardBisimulation ( NFTA < SymbolType, StateType > ( fta ) );
}
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > BackwardBisimulation::backwardBisimulation ( const automaton::NFTA < SymbolType, StateType > & fta ) {
    ext::set < ext::pair < StateType, StateType > > backwardBisimulation = initial ( fta.getStates ( ), { } );
 
    bool changed;
    do {
        changed = false;
 
        for ( const StateType & p : fta.getStates ( ) ) {
            for ( const StateType & q : fta.getStates ( ) ) {
                if ( ! backwardBisimulation.contains ( ext::make_pair ( p, q ) ) )
                    continue;
 
                for ( const std::pair < const ext::pair < common::ranked_symbol < SymbolType >, ext::vector < StateType > >, StateType > & pTransition : fta.getTransitionsToState ( p ) ) {
 
                    bool exists = false;
                    for ( const std::pair < const ext::pair < common::ranked_symbol < SymbolType >, ext::vector < StateType > >, StateType > & qTransition : fta.getTransitionsToState ( q ) ) {
                        if ( qTransition.first.first != pTransition.first.first )
                            continue;
 
                        size_t inRelation = 0;
                        for ( size_t i = 0; i < pTransition.first.second.size ( ); ++ i ) {
                            if ( backwardBisimulation.contains ( ext::make_pair ( pTransition.first.second [ i ], qTransition.first.second [ i ] ) ) )
                                ++ inRelation;
                        }
 
                        if ( inRelation == pTransition.first.second.size ( ) ) {
                            exists = true;
                            break;
                        }
                    }
 
                    if ( ! exists ) {
                        backwardBisimulation.erase ( ext::make_pair ( p, q ) );
                        backwardBisimulation.erase ( ext::make_pair ( q, p ) );
                        changed = true;
                        break;
                    }
                }
            }
        }
    } while ( changed );
 
    return backwardBisimulation;
}
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > BackwardBisimulation::backwardBisimulation ( const automaton::UnorderedDFTA < SymbolType, StateType > & fta ) {
    return backwardBisimulation ( UnorderedNFTA < SymbolType, StateType > ( fta ) );
}
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > BackwardBisimulation::backwardBisimulation ( const automaton::UnorderedNFTA < SymbolType, StateType > & fta ) {
    ext::set < ext::pair < StateType, StateType > > backwardBisimulation = initial ( fta.getStates ( ), { } );
 
    bool changed;
    do {
        changed = false;
 
        for ( const StateType & p : fta.getStates ( ) ) {
            for ( const StateType & q : fta.getStates ( ) ) {
                if ( ! backwardBisimulation.contains ( ext::make_pair ( p, q ) ) )
                    continue;
 
                for ( const std::pair < const ext::pair < common::ranked_symbol < SymbolType >, ext::multiset < StateType > >, StateType > & pTransition : fta.getTransitionsToState ( p ) ) {
 
                    ext::multiset < StateType > pSource;
                    for ( const StateType & state : pTransition.first.second ) {
                        auto lower = backwardBisimulation.lower_bound ( ext::slice_comp ( state ) );
                        pSource.insert ( lower->second );
                    }
 
                    bool exists = false;
                    for ( const std::pair < const ext::pair < common::ranked_symbol < SymbolType >, ext::multiset < StateType > >, StateType > & qTransition : fta.getTransitionsToState ( q ) ) {
                        if ( qTransition.first.first != pTransition.first.first )
                            continue;
 
                        ext::multiset < StateType > qSource;
                        for ( const StateType & state : qTransition.first.second ) {
                            auto lower = backwardBisimulation.lower_bound ( ext::slice_comp ( state ) );
                            qSource.insert ( lower->second );
                        }
 
                        if ( pSource == qSource ) {
                            exists = true;
                            break;
                        }
                    }
 
                    if ( ! exists ) {
                        backwardBisimulation.erase ( ext::make_pair ( p, q ) );
                        backwardBisimulation.erase ( ext::make_pair ( q, p ) );
                        changed = true;
                        break;
                    }
                }
            }
        }
    } while ( changed );
 
    return backwardBisimulation;
}
 
} /* namespace properties */
 
} /* namespace automaton */