computation of full left quotient finite automata

alib2algo/src/automaton/transform/AutomataLeftQuotientCartesianProduct.cpp

+/*
+ * AutomataLeftQuotientCartesianProduct.cpp
+ *
+ *  Created on: 20. 11. 2014
+ *	  Author: Tomas Pecka
+ */
+
+#include "AutomataLeftQuotientCartesianProduct.h"
+#include <registration/AlgoRegistration.hpp>
+
+namespace automaton {
+
+namespace transform {
+
+auto AutomataLeftQuotientCartesianProductNFA2 = registration::AbstractRegister < AutomataLeftQuotientCartesianProduct, automaton::MultiInitialStateNFA < DefaultSymbolType, ext::pair < DefaultStateType, DefaultStateType > >, const automaton::NFA < > &, const automaton::NFA < > &, bool > ( AutomataLeftQuotientCartesianProduct::quotient );
+
+
+} /* namespace transform */
+
+} /* namespace automaton */

alib2algo/src/automaton/transform/AutomataLeftQuotientCartesianProduct.h

+/*
+ * AutomataLeftQuotientCartesianProduct.h
+ *
+ * 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/>.
+ *
+ *  Created on: 20. 11. 2014
+ *	  Author: Tomas Pecka
+ */
+
+#ifndef AUTOMATA_LEFT_QUOTIENT_CARTESIAN_H_
+#define AUTOMATA_LEFT_QUOTIENT_CARTESIAN_H_
+
+#include <automaton/FSM/MultiInitialStateNFA.h>
+#include <queue>
+
+namespace automaton {
+
+namespace transform {
+
+/**
+ * Computation of the left quotient of languages represented by two finite automata.
+ * For finite automata A1, A2, we create a finite automaton A such that L(A) = \{ x : wx \in L(A2) and w \in L(A1) \}.
+ * Full quotient requires that w is maximal and x does not have prefix from L(A1). Non-full quotient does not require that to be true and only some prefix is removed from words in L(A2).
+ * This method utilizes cartesian product construction and it is described in paper "The Full Quotient and Its Closure Properties for Regular Languages".
+ */
+class AutomataLeftQuotientCartesianProduct {
+public:
+	/**
+	 * Divides (computes quotient of) two languages represented by two finite automata.
+	 * @tparam SymbolType Type for input symbols.
+	 * @tparam StateType1 Type for states in the first automaton.
+	 * @tparam StateType2 Type for states in the second automaton.
+	 * @param first First automaton (A1) representing language of the removed prefix
+	 * @param second Second automaton (A2) representing language from which the prefix is removed
+	 * @param full true if the resulting quotient should be full, false if not.
+	 * @return nondeterministic FA with multiple initial states representing the division (computed quotient) of two languages
+	 */
+	template < class SymbolType, class StateType1, class StateType2 >
+	static automaton::MultiInitialStateNFA < SymbolType, ext::pair < StateType1, StateType2 > > quotient(const automaton::NFA < SymbolType, StateType1 > & first, const automaton::NFA < SymbolType, StateType2 > & second, bool full);
+};
+
+template < class SymbolType, class StateType1, class StateType2 >
+automaton::MultiInitialStateNFA < SymbolType, ext::pair < StateType1, StateType2 > > AutomataLeftQuotientCartesianProduct::quotient(const automaton::NFA < SymbolType, StateType1 > & first, const automaton::NFA < SymbolType, StateType2 > & second, bool full) {
+	std::queue < ext::pair < StateType1, StateType2 > > queue;
+	queue.push ( ext::pair < StateType1, StateType2 > ( first.getInitialState ( ), second.getInitialState ( ) ) );
+
+	ext::set < ext::pair < StateType1, StateType2 > > Q;
+	ext::map < ext::pair < ext::pair < StateType1, StateType2 >, SymbolType >, ext::set < ext::pair < StateType1, StateType2 > > > delta;
+	ext::set < ext::pair < StateType1, StateType2 > > Q0;
+	ext::set < ext::pair < StateType1, StateType2 > > F;
+
+	while ( queue.size ( ) ) {
+		ext::pair < StateType1, StateType2 > state = std::move ( queue.front ( ) );
+		queue.pop ( );
+
+		if ( ! Q.count ( state ) ) {
+			Q.insert ( state );
+
+			if ( first.getFinalStates ( ).count ( state.first ) )
+				Q0.insert ( state );
+			if ( second.getFinalStates ( ).count ( state.second ) )
+				F.insert ( state );
+
+			for(const auto & tp : first.getTransitionsFromState ( state.first ) )
+				for(const auto & tq : second.getTransitionsFromState ( state.second ) )
+					if(tp.first.second == tq.first.second)
+						for(const auto & p : tp.second)
+							for(const auto & q : tq.second) {
+								if ( ! full || ! first.getFinalStates ( ).count ( p ) )
+									delta [ ext::make_pair ( state, tp.first.second ) ].insert ( ext::make_pair ( p, q ) );
+
+								queue.push ( ext::make_pair ( p, q ) ); // Note: the original paper kept this queue push statement included in body of the above condition. That is not correct.
+							}
+		}
+	}
+
+	automaton::MultiInitialStateNFA < SymbolType, ext::pair < StateType1, StateType2 > > res;
+
+	res.addInputSymbols(first.getInputAlphabet());
+	res.addInputSymbols(second.getInputAlphabet());
+
+	res.setStates ( Q );
+
+	for ( std::pair < ext::pair < ext::pair < StateType1, StateType2 >, SymbolType >, ext::set < ext::pair < StateType1, StateType2 > > > transitions : ext::make_mover ( delta ) ) {
+		res.addTransitions ( transitions.first.first, transitions.first.second, transitions.second );
+	}
+
+	res.setInitialStates ( Q0 );
+	res.setFinalStates ( F );
+
+	return res;
+}
+
+} /* namespace transform */
+
+} /* namespace automaton */
+
+#endif /* AUTOMATA_LEFT_QUOTIENT_CARTESIAN_H_ */