Minimize.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 <iomanip>
 
#include <ext/sstream>
 
#include <alib/map>
#include <alib/set>
 
#include <global/GlobalData.h>
 
#include <automaton/FSM/DFA.h>
#include <automaton/TA/DFTA.h>
 
namespace automaton {
 
namespace simplify {
 
class Minimize {
public:
    template < class SymbolType, class StateType >
    static automaton::DFA < SymbolType, StateType > minimize(const automaton::DFA < SymbolType, StateType >& dfa) {
        size_t steps;
        return minimize ( dfa, steps );
    }
 
    template < class SymbolType, class StateType >
    static automaton::DFA < SymbolType, StateType > minimize(const automaton::DFA < SymbolType, StateType >& dfa, size_t & steps);
 
    template < class SymbolType, class StateType >
    static automaton::DFTA < SymbolType, StateType > minimize(const automaton::DFTA < SymbolType, StateType >& dfta) {
        size_t steps;
        return minimize ( dfta, steps );
    }
 
    template < class SymbolType, class StateType >
    static automaton::DFTA < SymbolType, StateType > minimize(const automaton::DFTA < SymbolType, StateType >& dfta, size_t & steps);
 
private:
    template < class SymbolType, class StateType >
    static void print_progress(const automaton::DFA < SymbolType, StateType >& dfa, const ext::map<std::pair<StateType, ext::set<std::pair<SymbolType, StateType> > >, ext::set<StateType> >& minimizedTransitionFunction, size_t iter);
};
 
template < class SymbolType, class StateType >
automaton::DFA < SymbolType, StateType > Minimize::minimize(const automaton::DFA < SymbolType, StateType >& dfa, size_t & steps ) {
    steps = 0;
 
    if(dfa.getFinalStates().empty ( )) {
        automaton::DFA < SymbolType, StateType > result(dfa.getInitialState());
        result.setInputAlphabet(dfa.getInputAlphabet());
        return result;
    }
 
    ext::map<StateType, ext::map<SymbolType, StateType > > refactor;
 
    for(const StateType& state : dfa.getStates())
        refactor.insert(std::make_pair(state, ext::map<SymbolType, StateType>()));
 
    for(const std::pair<const ext::pair<StateType, SymbolType>, StateType>& transition : dfa.getTransitions())
        refactor[transition.first.first].insert(std::make_pair(transition.first.second, transition.second));
 
    ext::map<StateType, StateType> toEquivalentStates; //original state to equivalent state
    ext::map<std::pair<StateType, ext::set<std::pair<SymbolType, StateType> > >, ext::set<StateType> > minimizedTransitionFunction; //mapped to the original state
 
    const StateType *firstFinal = nullptr;
    const StateType *firstNonfinal = nullptr;
    for(const StateType& state : dfa.getStates()) {
        if(dfa.getFinalStates().count(state) == 0) { // not a final state
            if(!firstNonfinal)
                firstNonfinal = &state;
            toEquivalentStates.insert(std::pair<StateType, StateType>(state, *firstNonfinal));
        } else {
            if(!firstFinal)
                firstFinal = &state;
            toEquivalentStates.insert(std::pair<StateType, StateType>(state, *firstFinal));
        }
    }
 
    unsigned prevSize = 0;
    while ( true ) {
        for(const std::pair<const StateType, ext::map<SymbolType, StateType> >& transition : refactor) {
            const StateType& from = toEquivalentStates.find(transition.first)->second;
            ext::set<std::pair<SymbolType, StateType> > transitionFunction;
 
            for(const std::pair<const SymbolType, StateType> & transitionFromState : transition.second)
                transitionFunction.insert(std::make_pair(transitionFromState.first, toEquivalentStates.find(transitionFromState.second)->second));
 
            minimizedTransitionFunction[std::make_pair(from, transitionFunction)].insert(transition.first);
        }
 
        if(common::GlobalData::verbose)
            print_progress ( dfa, minimizedTransitionFunction, steps );
 
        if (minimizedTransitionFunction.size() == prevSize)
            break;
 
        prevSize = minimizedTransitionFunction.size();
        toEquivalentStates.clear();
 
        for(const std::pair<const std::pair<StateType, ext::set<std::pair<SymbolType, StateType> > >, ext::set<StateType> >& transition : minimizedTransitionFunction)
            for(const StateType& target : transition.second)
                toEquivalentStates.insert(std::make_pair(target, *(transition.second.begin())));
 
        minimizedTransitionFunction.clear();
 
        ++ steps;
    }
 
    auto findInitialGroup = [ ] ( const ext::map < std::pair < StateType, ext::set < std::pair < SymbolType, StateType > > >, ext::set < StateType > > & transitions, const StateType & initialState ) {
        for ( const std::pair < const std::pair < StateType, ext::set < std::pair < SymbolType, StateType > > >, ext::set < StateType > > & transition : transitions )
            if ( transition.second.count ( initialState ) )
                return transition.first.first;
        throw std::logic_error ( "Initial group not identified." );
    };
 
    automaton::DFA < SymbolType, StateType > result( findInitialGroup ( minimizedTransitionFunction, dfa.getInitialState ( ) ) );
 
    result.setInputAlphabet(dfa.getInputAlphabet());
 
    for(const std::pair<const std::pair<StateType, ext::set<std::pair<SymbolType, StateType> > >, ext::set<StateType> >& transition : minimizedTransitionFunction) {
        result.addState(transition.first.first);
        if(dfa.getFinalStates().count(transition.first.first))
            result.addFinalState(transition.first.first);
    }
 
    for(const std::pair<const std::pair<StateType, ext::set<std::pair<SymbolType, StateType> > >, ext::set<StateType> >& transition : minimizedTransitionFunction)
        for(const std::pair<SymbolType, StateType>& transitionFromState : transition.first.second)
            result.addTransition(transition.first.first, transitionFromState.first, transitionFromState.second);
 
    return result;
}
 
#define RESETSS(x) {(x).clear(); (x).str("");}
 
template < class SymbolType, class StateType >
void Minimize::print_progress(const automaton::DFA < SymbolType, StateType >& dfa, const ext::map<std::pair<StateType, ext::set<std::pair<SymbolType, StateType> > >, ext::set<StateType> >& minimizedTransitionFunction, size_t iter) {
    common::Streams::log << "delta " << iter << std::endl;
 
    //ext::map<std::pair<StateType, ext::set<std::pair<SymbolType, StateType> > >, ext::set<StateType> > minimizedTransitionFunction; //mapped to the original state
 
    /* need to restruct this first so we have table like:   orig state | new state | trans_symb_1 | trans_symb_2 | ... | trans_symb_n */
    // we surely have DFA here (transition map hence)
    ext::map<std::pair<StateType, StateType>, ext::map<SymbolType, StateType>> printMap;
    for(const auto& kv: minimizedTransitionFunction) {
        for(const auto& state : kv.second) {
            ext::map<SymbolType, StateType> stateTransMap;
            for(const auto& transition : kv.first.second) {
                stateTransMap.insert(std::make_pair(transition.first, transition.second));
            }
            printMap.insert(std::make_pair(std::make_pair(state, kv.first.first), stateTransMap));
        }
    }
 
    size_t stateWidth = 1;
    size_t stateMapWidth = 1;
    ext::map<SymbolType, size_t> colWidths;
    ext::ostringstream ss;
 
    for(const SymbolType& symbol : dfa.getInputAlphabet()) {
        ss << symbol;
        colWidths[symbol] = ss.str().size();
        RESETSS(ss);
    }
    for(const auto& kv : printMap) {
        ss << kv.first.first;
        stateWidth = std::max(stateWidth, ss.str().size());
        RESETSS(ss);
 
        ss << kv.first.second;
        stateMapWidth = std::max(stateMapWidth, ss.str().size());
        RESETSS(ss);
 
        for(const SymbolType& symbol : dfa.getInputAlphabet()) {
            auto it = kv.second.find(symbol);
            if(it != kv.second.end()) {
                ss << it -> second;
                colWidths[symbol] = std::max(colWidths[symbol], ss.str().size());
                RESETSS(ss);
            }
        }
    }
 
    common::Streams::log << std::setw(stateWidth) << "";
    common::Streams::log << " | ";
    common::Streams::log << std::setw(stateMapWidth) << "";
    common::Streams::log << " | ";
    for(const SymbolType& symbol : dfa.getInputAlphabet()) {
        ss << symbol;
        common::Streams::log << std::setw(colWidths[symbol]) << ss.str() << " | ";
        RESETSS(ss);
    }
    common::Streams::log << std::endl;
    for(const auto& kv : printMap) {
        ss << kv.first.first;
        common::Streams::log << std::setw(stateWidth) << ss.str() << " | ";
        RESETSS(ss);
 
        ss << kv.first.second;
        common::Streams::log << std::setw(stateMapWidth) << ss.str() << " | ";
        RESETSS(ss);
 
        for(const auto& symbol : dfa.getInputAlphabet()) {
            auto it = kv.second.find(symbol);
            if(it != kv.second.end()) {
                ss << it -> second;
                common::Streams::log << std::setw(colWidths[symbol]) << ss.str();
                RESETSS(ss);
            }
            else {
                common::Streams::log << std::setw(colWidths[symbol]) << "";
            }
            common::Streams::log << " | ";
        }
        common::Streams::log << std::endl;
    }
    common::Streams::log << std::endl;
}
 
template < class SymbolType, class StateType >
automaton::DFTA < SymbolType, StateType > Minimize::minimize(const automaton::DFTA < SymbolType, StateType >& dfta, size_t & steps ) {
    automaton::DFTA<SymbolType, StateType> result;
    result.setInputAlphabet(dfta.getInputAlphabet());
 
    if (dfta.getFinalStates().empty ( ))
        return result;
 
    typedef std::pair < const ext::pair < common::ranked_symbol < SymbolType >, ext::vector < StateType > >, StateType > Transition;
 
    ext::map < StateType, ext::map < Transition, ext::vector < size_t > > > stateOccurences;
 
    for (const auto & state : dfta.getStates())
        stateOccurences[state];
 
    for(auto & transition : dfta.getTransitions()) {
        const ext::vector<StateType> & from = transition.first.second;
        for (size_t i = 0; i < from.size ( ); ++i)
            stateOccurences[from[i]][transition].push_back(i);
    }
 
    ext::map <StateType, StateType> toEquivalentStates;
    ext::map<std::pair<StateType, ext::map<ext::tuple<common::ranked_symbol<SymbolType>, ext::vector<StateType>, StateType >, ext::set < size_t > > >, ext::set<StateType> > minimizedTransitionFunction; //mapped to the original states
    const StateType *firstFinal = nullptr;
    const StateType *firstNonfinal = nullptr;
    for (const StateType &state : dfta.getStates()) {
        if (dfta.getFinalStates().count(state) == 0) { // not a final state
            if (!firstNonfinal)
                firstNonfinal = &state;
 
            toEquivalentStates.insert(std::pair<StateType, StateType>(state, *firstNonfinal));
        } else {
            if (!firstFinal)
                firstFinal = &state;
 
            toEquivalentStates.insert(std::pair<StateType, StateType>(state, *firstFinal));
        }
    }
 
    unsigned prevSize = 0;
    steps = 0;
    while(true) {
        for(const auto & occurencesOfState : stateOccurences) {
            const StateType & state = occurencesOfState.first;
            const StateType & equivalentState = toEquivalentStates.find(state) -> second;
            ext::map<ext::tuple<common::ranked_symbol<SymbolType>, ext::vector<StateType>, StateType >, ext::set<size_t> > keyTransitionsPart;
 
            for(const auto & transitionOccurences : occurencesOfState.second) {
                const auto & transition = transitionOccurences.first;
                for ( size_t i : transitionOccurences.second) {
                    ext::vector<StateType> fromWithoutCurrent (transition.first.second);
                    fromWithoutCurrent.erase(fromWithoutCurrent.begin()+i);
                    keyTransitionsPart[ext::make_tuple(transition.first.first, fromWithoutCurrent, toEquivalentStates.find(transition.second)->second)].insert(i);
                }
            }
 
            minimizedTransitionFunction [ std::make_pair ( equivalentState, keyTransitionsPart ) ].insert(state);
        }
 
        if (minimizedTransitionFunction.size() == prevSize)
            break;
 
        prevSize = minimizedTransitionFunction.size();
        toEquivalentStates.clear();
        for(const auto & transition : minimizedTransitionFunction)
            for(const StateType & target : transition.second)
                toEquivalentStates.insert(std::make_pair ( target, * transition.second.begin() ) );
 
        minimizedTransitionFunction.clear();
 
        ++ steps;
    }
 
    for (const auto & transition : minimizedTransitionFunction) {
        const auto & state = *(transition.second.begin());
        result.addState(state);
        if(dfta.getFinalStates().count(state))
            result.addFinalState(state);
    }
 
    for(const auto & transition : dfta.getTransitions()) {
        ext::vector<StateType> from;
        from.reserve(transition.first.second.size());
        for (const StateType & state : transition.first.second)
            from.push_back(toEquivalentStates.find(state)->second);
 
        result.addTransition(transition.first.first, from, toEquivalentStates.find(transition.second)->second);
    }
 
    return result;
}
 
} /* namespace simplify */
 
} /* namespace automaton */