NFA.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/multimap>
#include <alib/set>
 
#include <core/components.hpp>
 
#include <common/DefaultStateType.h>
#include <common/DefaultSymbolType.h>
 
#include <automaton/AutomatonException.h>
 
#include <core/normalize.hpp>
#include <alphabet/common/SymbolNormalize.h>
#include <automaton/common/AutomatonNormalize.h>
 
#include "DFA.h"
 
namespace automaton {
 
class InputAlphabet;
class States;
class FinalStates;
class InitialState;
 
template < class SymbolTypeT = DefaultSymbolType, class StateTypeT = DefaultStateType >
class NFA final : public core::Components < NFA < SymbolTypeT, StateTypeT >, ext::set < SymbolTypeT >, component::Set, InputAlphabet, ext::set < StateTypeT >, component::Set, std::tuple < States, FinalStates >, StateTypeT, component::Value, InitialState > {
public:
    typedef SymbolTypeT SymbolType;
    typedef StateTypeT StateType;
 
private:
    ext::multimap < ext::pair < StateType, SymbolType >, StateType> transitions;
 
public:
    explicit NFA ( StateType initialState );
 
    explicit NFA ( ext::set < StateType > states, ext::set < SymbolType > inputAlphabet, StateType initialState, ext::set < StateType > finalStates );
 
    /*
     * \brief Creates a new instance of the automaton based on the Deterministic finite automaton.
     *
     * \param other the Deterministic finite automaton
     */
    explicit NFA ( const DFA < SymbolType, StateType > & other );
 
    const StateType & getInitialState ( ) const & {
        return this->template accessComponent < InitialState > ( ).get ( );
    }
 
    StateType && getInitialState ( ) && {
        return std::move ( this->template accessComponent < InitialState > ( ).get ( ) );
    }
 
    bool setInitialState ( StateType state ) {
        return this->template accessComponent < InitialState > ( ).set ( std::move ( state ) );
    }
 
    const ext::set < StateType > & getStates ( ) const & {
        return this->template accessComponent < States > ( ).get ( );
    }
 
    ext::set < StateType > && getStates ( ) && {
        return std::move ( this->template accessComponent < States > ( ).get ( ) );
    }
 
    bool addState ( StateType state ) {
        return this->template accessComponent < States > ( ).add ( std::move ( state ) );
    }
 
    void setStates ( ext::set < StateType > states ) {
        this->template accessComponent < States > ( ).set ( std::move ( states ) );
    }
 
    void removeState ( const StateType & state ) {
        this->template accessComponent < States > ( ).remove ( state );
    }
 
    const ext::set < StateType > & getFinalStates ( ) const & {
        return this->template accessComponent < FinalStates > ( ).get ( );
    }
 
    ext::set < StateType > && getFinalStates ( ) && {
        return std::move ( this->template accessComponent < FinalStates > ( ).get ( ) );
    }
 
    bool addFinalState ( StateType state ) {
        return this->template accessComponent < FinalStates > ( ).add ( std::move ( state ) );
    }
 
    void setFinalStates ( ext::set < StateType > states ) {
        this->template accessComponent < FinalStates > ( ).set ( std::move ( states ) );
    }
 
    void removeFinalState ( const StateType & state ) {
        this->template accessComponent < FinalStates > ( ).remove ( state );
    }
 
    const ext::set < SymbolType > & getInputAlphabet ( ) const & {
        return this->template accessComponent < InputAlphabet > ( ).get ( );
    }
 
    ext::set < SymbolType > && getInputAlphabet ( ) && {
        return std::move ( this->template accessComponent < InputAlphabet > ( ).get ( ) );
    }
 
    bool addInputSymbol ( SymbolType symbol ) {
        return this->template accessComponent < InputAlphabet > ( ).add ( std::move ( symbol ) );
    }
 
    void addInputSymbols ( ext::set < SymbolType > symbols ) {
        this->template accessComponent < InputAlphabet > ( ).add ( std::move ( symbols ) );
    }
 
    void setInputAlphabet ( ext::set < SymbolType > symbols ) {
        this->template accessComponent < InputAlphabet > ( ).set ( std::move ( symbols ) );
    }
 
    void removeInputSymbol ( const SymbolType & symbol ) {
        this->template accessComponent < InputAlphabet > ( ).remove ( symbol );
    }
 
    bool addTransition ( StateType from, SymbolType input, StateType to );
 
    bool removeTransition ( const StateType & from, const SymbolType & input, const StateType & to );
 
    const ext::multimap < ext::pair < StateType, SymbolType >, StateType > & getTransitions ( ) const &;
 
    ext::multimap < ext::pair < StateType, SymbolType >, StateType > && getTransitions ( ) &&;
 
    auto getTransitionsFromState ( const StateType & from ) const;
 
    ext::multimap < ext::pair < StateType, SymbolType >, StateType > getTransitionsToState ( const StateType & to ) const;
 
    bool isDeterministic ( ) const;
 
    bool isTotal ( ) const;
 
    auto operator <=> ( const NFA & other ) const {
        return std::tie ( getStates ( ), getInputAlphabet ( ), getInitialState ( ), getFinalStates ( ), transitions ) <=> std::tie ( other.getStates ( ), other.getInputAlphabet ( ), other.getInitialState ( ), other.getFinalStates ( ), other.getTransitions ( ) );
    }
 
    bool operator == ( const NFA & other ) const {
        return std::tie ( getStates ( ), getInputAlphabet ( ), getInitialState ( ), getFinalStates ( ), transitions ) == std::tie ( other.getStates ( ), other.getInputAlphabet ( ), other.getInitialState ( ), other.getFinalStates ( ), other.getTransitions ( ) );
    }
 
    friend ext::ostream & operator << ( ext::ostream & out, const NFA & instance ) {
        return out << "(NFA"
               << " states = " << instance.getStates ( )
               << " inputAlphabet = " << instance.getInputAlphabet ( )
               << " initialState = " << instance.getInitialState ( )
               << " finalStates = " << instance.getFinalStates ( )
               << " transitions = " << instance.getTransitions ( )
               << ")";
    }
};
 
template < class T >
class isNFA_impl : public std::false_type {};
 
template < class SymbolType, class StateType >
class isNFA_impl < NFA < SymbolType, StateType > > : public std::true_type {};
 
template < class T >
constexpr bool isNFA = isNFA_impl < T > { };
 
template<class SymbolType, class StateType >
NFA < SymbolType, StateType >::NFA ( ext::set < StateType > states, ext::set < SymbolType > inputAlphabet, StateType initialState, ext::set < StateType > finalStates ) : core::Components < NFA, ext::set < SymbolType >, component::Set, InputAlphabet, ext::set < StateType >, component::Set, std::tuple < States, FinalStates >, StateType, component::Value, InitialState > ( std::move ( inputAlphabet ), std::move ( states ), std::move ( finalStates ), std::move ( initialState ) ) {
}
 
template<class SymbolType, class StateType >
NFA < SymbolType, StateType >::NFA ( StateType initialState ) : NFA ( ext::set < StateType > { initialState }, ext::set < SymbolType > { }, initialState, ext::set < StateType > { } ) {
}
 
template<class SymbolType, class StateType >
NFA < SymbolType, StateType >::NFA ( const DFA < SymbolType, StateType > & other ) : NFA ( other.getStates ( ), other.getInputAlphabet ( ), other.getInitialState ( ), other.getFinalStates ( ) ) {
    transitions.insert ( other.getTransitions ( ).begin ( ), other.getTransitions ( ).end ( ) );
}
 
template<class SymbolType, class StateType >
bool NFA < SymbolType, StateType >::addTransition ( StateType from, SymbolType input, StateType to ) {
    if ( ! getStates ( ).contains ( from ) )
        throw AutomatonException ( "State \"" + ext::to_string ( from ) + "\" doesn't exist." );
 
    if ( ! getInputAlphabet ( ).contains ( input ) )
        throw AutomatonException ( "Input symbol \"" + ext::to_string ( input ) + "\" doesn't exist." );
 
    if ( ! getStates ( ).contains ( to ) )
        throw AutomatonException ( "State \"" + ext::to_string ( to ) + "\" doesn't exist." );
 
    auto upper_bound = transitions.upper_bound ( ext::tie ( from, input ) );
    auto lower_bound = transitions.lower_bound ( ext::tie ( from, input ) );
    auto iter = std::lower_bound ( lower_bound, upper_bound, to, [ ] ( const auto & transition, const auto & target ) { return transition.second < target; } );
    if ( iter != upper_bound && to >= iter->second )
        return false;
 
    ext::pair < StateType, SymbolType > key = ext::make_pair ( std::move ( from ), std::move ( input ) );
    transitions.insert ( iter, std::make_pair ( std::move ( key ), std::move ( to ) ) );
    return true;
}
 
template<class SymbolType, class StateType >
bool NFA < SymbolType, StateType >::removeTransition ( const StateType & from, const SymbolType & input, const StateType & to ) {
    auto upper_bound = transitions.upper_bound ( ext::tie ( from, input ) );
    auto lower_bound = transitions.lower_bound ( ext::tie ( from, input ) );
    auto iter = std::find_if ( lower_bound, upper_bound, [ & ] ( const auto & transition ) { return transition.second == to; } );
    if ( iter == upper_bound )
        return false;
 
    transitions.erase ( iter );
    return true;
}
 
template<class SymbolType, class StateType >
const ext::multimap < ext::pair < StateType, SymbolType >, StateType > & NFA < SymbolType, StateType >::getTransitions ( ) const & {
    return transitions;
}
 
template<class SymbolType, class StateType >
ext::multimap < ext::pair < StateType, SymbolType >, StateType > && NFA < SymbolType, StateType >::getTransitions ( ) && {
    return std::move ( transitions );
}
 
template<class SymbolType, class StateType >
auto NFA < SymbolType, StateType >::getTransitionsFromState ( const StateType & from ) const {
    if ( ! getStates ( ).contains ( from ) )
        throw AutomatonException ( "State \"" + ext::to_string ( from ) + "\" doesn't exist" );
 
    return transitions.equal_range ( ext::slice_comp ( from ) );
}
 
template<class SymbolType, class StateType >
ext::multimap < ext::pair < StateType, SymbolType >, StateType > NFA < SymbolType, StateType >::getTransitionsToState ( const StateType & to ) const {
    if ( ! getStates ( ).contains ( to ) )
        throw AutomatonException ( "State \"" + ext::to_string ( to ) + "\" doesn't exist" );
 
    ext::multimap < ext::pair < StateType, SymbolType >, StateType > transitionsToState;
 
    for ( const std::pair < const ext::pair < StateType, SymbolType >, StateType > & transition : transitions )
        if ( transition.second == to )
            transitionsToState.insert ( transition );
 
    return transitionsToState;
}
 
template<class SymbolType, class StateType >
bool NFA < SymbolType, StateType >::isDeterministic ( ) const {
    if ( transitions.empty ( ) )
        return true;
 
    for ( auto iter = transitions.begin ( ); std::next ( iter ) != transitions.end ( ); ++ iter )
        if ( iter->first == std::next ( iter )->first )
            return false;
 
    return true;
}
 
template<class SymbolType, class StateType >
bool NFA < SymbolType, StateType >::isTotal ( ) const {
    for ( const StateType & state : getStates ( ) ) {
        for ( const SymbolType & symbol : getInputAlphabet ( ) ) {
            if ( ! getTransitions ( ).contains ( ext::make_pair ( state, symbol ) ) )
                return false;
        }
    }
    return true;
}
 
} /* namespace automaton */
 
namespace core {
 
template<class SymbolType, class StateType >
class SetConstraint< automaton::NFA < SymbolType, StateType >, SymbolType, automaton::InputAlphabet > {
public:
    static bool used ( const automaton::NFA < SymbolType, StateType > & automaton, const SymbolType & symbol ) {
        for ( const std::pair < const ext::pair < StateType, SymbolType >, StateType > & transition : automaton.getTransitions ( ) )
            if ( transition.first.second == symbol )
                return true;
 
        return false;
    }
 
    static bool available ( const automaton::NFA < SymbolType, StateType > &, const SymbolType & ) {
        return true;
    }
 
    static void valid ( const automaton::NFA < SymbolType, StateType > &, const SymbolType & ) {
    }
};
 
template<class SymbolType, class StateType >
class SetConstraint< automaton::NFA < SymbolType, StateType >, StateType, automaton::States > {
public:
    static bool used ( const automaton::NFA < SymbolType, StateType > & automaton, const StateType & state ) {
        if ( automaton.getInitialState ( ) == state )
            return true;
 
        if ( automaton.getFinalStates ( ).contains ( state ) )
            return true;
 
        for ( const std::pair < const ext::pair < StateType, SymbolType >, StateType > & transition : automaton.getTransitions ( ) )
            if ( ( transition.first.first == state ) || transition.second == state )
                return true;
 
        return false;
    }
 
    static bool available ( const automaton::NFA < SymbolType, StateType > &, const StateType & ) {
        return true;
    }
 
    static void valid ( const automaton::NFA < SymbolType, StateType > &, const StateType & ) {
    }
};
 
template<class SymbolType, class StateType >
class SetConstraint< automaton::NFA < SymbolType, StateType >, StateType, automaton::FinalStates > {
public:
    static bool used ( const automaton::NFA < SymbolType, StateType > &, const StateType & ) {
        return false;
    }
 
    static bool available ( const automaton::NFA < SymbolType, StateType > & automaton, const StateType & state ) {
        return automaton.template accessComponent < automaton::States > ( ).get ( ).contains ( state );
    }
 
    static void valid ( const automaton::NFA < SymbolType, StateType > &, const StateType & ) {
    }
};
 
template<class SymbolType, class StateType >
class ElementConstraint< automaton::NFA < SymbolType, StateType >, StateType, automaton::InitialState > {
public:
    static bool available ( const automaton::NFA < SymbolType, StateType > & automaton, const StateType & state ) {
        return automaton.template accessComponent < automaton::States > ( ).get ( ).contains ( state );
    }
 
    static void valid ( const automaton::NFA < SymbolType, StateType > &, const StateType & ) {
    }
};
 
template < class SymbolType, class StateType >
struct normalize < automaton::NFA < SymbolType, StateType > > {
    static automaton::NFA < > eval ( automaton::NFA < SymbolType, StateType > && value ) {
        ext::set < DefaultSymbolType > alphabet = alphabet::SymbolNormalize::normalizeAlphabet ( std::move ( value ).getInputAlphabet ( ) );
        ext::set < DefaultStateType > states = automaton::AutomatonNormalize::normalizeStates ( std::move ( value ).getStates ( ) );
        DefaultStateType initialState = automaton::AutomatonNormalize::normalizeState ( std::move ( value ).getInitialState ( ) );
        ext::set < DefaultStateType > finalStates = automaton::AutomatonNormalize::normalizeStates ( std::move ( value ).getFinalStates ( ) );
 
        automaton::NFA < > res ( std::move ( states ), std::move ( alphabet ), std::move ( initialState ), std::move ( finalStates ) );
 
        for ( std::pair < ext::pair < StateType, SymbolType >, StateType > && transition : ext::make_mover ( std::move ( value ).getTransitions ( ) ) ) {
            DefaultStateType from = automaton::AutomatonNormalize::normalizeState ( std::move ( transition.first.first ) );
            DefaultSymbolType input = alphabet::SymbolNormalize::normalizeSymbol ( std::move ( transition.first.second ) );
            DefaultStateType target = automaton::AutomatonNormalize::normalizeState ( std::move ( transition.second ) );
 
            res.addTransition ( std::move ( from ), std::move ( input ), std::move ( target ) );
        }
 
        return res;
    }
};
 
} /* namespace core */
 
extern template class automaton::NFA < >;