DistinguishableStates.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/FSM/DFA.h>
#include <automaton/TA/DFTA.h>
 
#include <automaton/TA/UnorderedDFTA.h>
 
namespace automaton {
 
namespace properties {
 
class DistinguishableStates {
    template < class StateType >
    static ext::set < ext::pair < StateType, StateType > > initial ( const ext::set < StateType > & states, const ext::set < StateType > & finals ) {
        ext::set < ext::pair < StateType, StateType > > init;
 
        for ( const StateType & a : states ) {
            for ( const StateType & b : states ) {
                if ( finals.count ( a ) != finals.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 > > distinguishable ( const automaton::DFA < SymbolType, StateType > & fsm );
 
    template < class SymbolType, class StateType >
    static ext::set < ext::pair < StateType, StateType > > distinguishable ( const automaton::DFTA < SymbolType, StateType > & fta );
 
    template < class SymbolType, class StateType >
    static ext::set < ext::pair < StateType, StateType > > distinguishable ( const automaton::UnorderedDFTA < SymbolType, StateType > & fta );
};
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > DistinguishableStates::distinguishable ( const automaton::DFA < SymbolType, StateType > & fsm ) {
    ext::set < ext::pair < StateType, StateType > > distinguishable = initial ( fsm.getStates ( ), fsm.getFinalStates ( ) );
 
    bool changed;
    do {
        changed = false;
 
        for ( const StateType & a : fsm.getStates ( ) ) {
            for ( const StateType & b : fsm.getStates ( ) ) {
                if ( distinguishable.count ( ext::make_pair ( a, b ) ) ) // we have not yet found this
                    continue;
 
                for ( const SymbolType & symb : fsm.getInputAlphabet ( ) ) {
                    auto trA = fsm.getTransitions ( ).find ( ext::make_pair ( a, symb ) );
                    auto trB = fsm.getTransitions ( ).find ( ext::make_pair ( b, symb ) );
 
                    if ( trA == fsm.getTransitions ( ).end ( ) && trB == fsm.getTransitions ( ).end ( ) ) {
                        // end up in the same target state (dead state) -> not distinguishable
                    } else if ( trA == fsm.getTransitions ( ).end ( ) || trB == fsm.getTransitions ( ).end ( ) || distinguishable.count ( ext::make_pair ( trA -> second, trB -> second ) ) ) {
                        // end up in dead state  - dead state is be distinguishable from every other state OR
                        // end up in distinguishable states
                        distinguishable.insert ( ext::make_pair ( a, b ) );
                        distinguishable.insert ( ext::make_pair ( b, a ) );
                        changed = true;
                    }
                }
            }
        }
 
    } while ( changed );
 
    return distinguishable;
}
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > DistinguishableStates::distinguishable ( const automaton::DFTA < SymbolType, StateType > & fta ) {
    ext::set < ext::pair < StateType, StateType > > distinguishable = initial ( fta.getStates ( ), fta.getFinalStates ( ) );
 
    bool changed;
    do {
        changed = false;
 
        for ( const StateType & a : fta.getStates ( ) ) {
            for ( const StateType & b : fta.getStates ( ) ) {
                if ( distinguishable.count ( ext::make_pair ( a, b ) ) )
                    continue;
 
                for ( const std::pair < const ext::pair < common::ranked_symbol < SymbolType >, ext::vector < StateType > >, StateType > & transition : fta.getTransitions ( ) ) {
                    for ( size_t i = 0; i < transition.first.second.size ( ); ++ i ) {
                        if ( transition.first.second [ i ] == a ) {
                            ext::vector < StateType > copy = transition.first.second;
                            copy [ i ] = b;
 
                            const auto & transition2 = fta.getTransitions ( ).find ( std::make_pair ( transition.first.first, std::move ( copy ) ) );
 
                            if ( transition2 == fta.getTransitions ( ).end ( ) || distinguishable.count ( ext::make_pair ( transition.second, transition2->second ) ) ) {
                                // end up in dead state - dead state is be distinguishable from every other state OR
                                // end up in distinguishable states
                                distinguishable.insert ( ext::make_pair ( a, b ) );
                                distinguishable.insert ( ext::make_pair ( b, a ) );
                                changed = true;
                            }
                        }
                    }
                }
            }
        }
    } while ( changed );
 
    return distinguishable;
}
 
template < class SymbolType, class StateType >
ext::set < ext::pair < StateType, StateType > > DistinguishableStates::distinguishable ( const automaton::UnorderedDFTA < SymbolType, StateType > & fta ) {
    ext::set < ext::pair < StateType, StateType > > distinguishable = initial ( fta.getStates ( ), fta.getFinalStates ( ) );
 
    bool changed;
    do {
        changed = false;
 
        for ( const StateType & a : fta.getStates ( ) ) {
            for ( const StateType & b : fta.getStates ( ) ) {
                if ( distinguishable.count ( ext::make_pair ( a, b ) ) )
                    continue;
 
                for ( const std::pair < const ext::pair < common::ranked_symbol < SymbolType >, ext::multiset < StateType > >, StateType > & transition : fta.getTransitions ( ) ) {
                    for ( const StateType & state : transition.first.second ) {
                        if ( state == a ) {
                            ext::multiset < StateType > copy = transition.first.second;
                            copy.erase ( copy.find ( state ) );
                            copy.insert ( b );
 
                            const auto & transition2 = fta.getTransitions ( ).find ( std::make_pair ( transition.first.first, std::move ( copy ) ) );
 
                            if ( transition2 == fta.getTransitions ( ).end ( ) || distinguishable.count ( ext::make_pair ( transition.second, transition2->second ) ) ) {
                                // end up in dead state - dead state is be distinguishable from every other state OR
                                // end up in distinguishable states
                                distinguishable.insert ( ext::make_pair ( a, b ) );
                                distinguishable.insert ( ext::make_pair ( b, a ) );
                                changed = true;
                            }
                        }
                    }
                }
            }
        }
    } while ( changed );
 
    return distinguishable;
}
 
} /* namespace properties */
 
} /* namespace automaton */