Bisimulation.java

/*
 * (C) Copyright 2005 Arnaud Bailly (arnaud.oqube@gmail.com),
 *     Yves Roos (yroos@lifl.fr) and others.
 *
 * Licensed under the Apache License, Version 2.0 (the License);
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an AS IS BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package rationals.properties;

import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Set;

import rationals.Automaton;
import rationals.Builder;
import rationals.Couple;
import rationals.State;
import rationals.Transition;

/**
 * This method computes the (strong) bisimulation relation between two states.
 * 
 * @version $Id: Bisimulation.java 2 2006-08-24 14:41:48Z oqube $
 */
public class Bisimulation<L, Tr extends Transition<L>, T extends Builder<L, Tr, T>> implements Relation<L, Tr, T> {

    private Automaton<L, Tr, T> a1;

    private Automaton<L, Tr, T> a2;

    private Set<Couple> exp;

    /**
     * Constructor with two automaton.
     * This constructor effectively calls {@link setAutomata(Automaton,Automaton)}.
     * 
     * @param automaton
     * @param automaton2
     */
    public Bisimulation(Automaton<L, Tr, T> automaton, Automaton<L, Tr, T> automaton2) {
        setAutomata(automaton,automaton2);
    }

    /**
     * Argument-less constructor.
     * Note that this implies the method {@link setAutomata(Automaton,Automaton)} 
     * <strong>must</strong> be called before using this relation.
     */
    public Bisimulation() {
    }

    /*
     * (non-Javadoc)
     * 
     * @see rationals.tests.Relation#setAutomata(rationals.Automaton,
     *      rationals.Automaton)
     */
    public void setAutomata(Automaton<L, Tr, T> a1, Automaton<L, Tr, T> a2) {
        this.a1 = a1;
        this.a2 = a2;
        this.exp = new HashSet<>();
    }

    /*
     * (non-Javadoc)
     * 
     * @see rationals.tests.Relation#equivalence(rationals.State,
     *      rationals.State)
     */
    public boolean equivalence(State q0a, State q0b) {
        Couple cpl = new Couple(q0a, q0b);
        /* check states are unknown */
        if (exp.contains(cpl))
            return true;
        exp.add(cpl);
        /* iterate over all transitions */
        Set<Transition<L>> tas = a1.delta(q0a);
        Set<Transition<L>> tbs = a2.delta(q0b);
        Iterator<Transition<L>> it = tas.iterator();
        while (it.hasNext()) {
            Transition<L> tr = it.next();
            State ea = tr.end();
            /* check transition exists in b */
            Set<Transition<L>> tbsl = a2.delta(q0b, tr.label());
            if (tbsl.isEmpty())
                return false;
            Iterator<Transition<L>> trb = tbsl.iterator();
            while (trb.hasNext()) {
                Transition<L> tb = trb.next();
                /* mark transition as visited */
                tbs.remove(tb);
                State eb = tb.end();
                if (!equivalence(ea, eb) && !trb.hasNext())
                    return false;
            }
        }
        /* checks all transitions from b has been visited */
        if (!tbs.isEmpty()) {
            exp.remove(cpl);
            return false;
        }
        /* OK */
        return true;
    }

    /**
     * Checks that all combination of states from nsa and nsb
     * are bisimilar.
     * 
     */
    public boolean equivalence(Set<State> nsa, Set<State> nsb) {
       for(Iterator<State> i = nsa.iterator();i.hasNext();) {
           State sa = i.next();
           for(Iterator<State> j = nsb.iterator();j.hasNext();) {
               State sb = j.next();
               if(!equivalence(sa,sb))
                   return false;
           }
       }
       return true;
    }
    
    /* (non-Javadoc)
     * @see rationals.properties.Relation#getErrorTrace()
     */
    public List<L> getErrorTrace() {
        throw new UnsupportedOperationException();
    }
}