GateTranslator

/*******************************************************************************
 * SAT4J: a SATisfiability library for Java Copyright (C) 2004-2008 Daniel Le Berre
 *
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * http://www.eclipse.org/legal/epl-v10.html
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either the GNU Lesser General Public License Version 2.1 or later (the
 * "LGPL"), in which case the provisions of the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of the LGPL, and not to allow others to use your version of
 * this file under the terms of the EPL, indicate your decision by deleting
 * the provisions above and replace them with the notice and other provisions
 * required by the LGPL. If you do not delete the provisions above, a recipient
 * may use your version of this file under the terms of the EPL or the LGPL.
 *
 * Based on the original MiniSat specification from:
 *
 * An extensible SAT solver. Niklas Een and Niklas Sorensson. Proceedings of the
 * Sixth International Conference on Theory and Applications of Satisfiability
 * Testing, LNCS 2919, pp 502-518, 2003.
 *
 * See www.minisat.se for the original solver in C++.
 *
 *******************************************************************************/
package org.sat4j.tools;

import java.math.BigInteger;

import org.sat4j.core.Vec;
import org.sat4j.core.VecInt;
import org.sat4j.specs.ContradictionException;
import org.sat4j.specs.IConstr;
import org.sat4j.specs.ISolver;
import org.sat4j.specs.IVec;
import org.sat4j.specs.IVecInt;

/**
 * Utility class to easily feed a SAT solver using logical gates.
 *
 * @author leberre
 *
 */
public class GateTranslator extends SolverDecorator<ISolver> {

	/**
     *
     */
	private static final long serialVersionUID = 1L;

	public GateTranslator(ISolver solver) {
		super(solver);
	}

	/**
	 * translate y <=> FALSE into a clause.
	 *
	 * @param y
	 *            a variable to falsify
	 * @throws ContradictionException
	 *             iff a trivial inconsistency is found.
	 * @since 2.1
	 */
	public IConstr gateFalse(int y) throws ContradictionException {
		IVecInt clause = new VecInt(2);
		clause.push(-y);
		return processClause(clause);
	}

	/**
	 * translate y <=> TRUE into a clause.
	 *
	 * @param y
	 *            a variable to verify
	 * @throws ContradictionException
	 * @since 2.1
	 */
	public IConstr gateTrue(int y) throws ContradictionException {
		IVecInt clause = new VecInt(2);
		clause.push(y);
		return processClause(clause);
	}

	/**
	 * translate y <=> if x1 then x2 else x3 into clauses.
	 *
	 * @param y
	 * @param x1
	 *            the selector variable
	 * @param x2
	 * @param x3
	 * @throws ContradictionException
	 * @since 2.1
	 */
	public IConstr[] ite(int y, int x1, int x2, int x3)
			throws ContradictionException {
		IConstr[] constrs = new IConstr[6];
		IVecInt clause = new VecInt(5);
		// y <=> (x1 -> x2) and (not x1 -> x3)
		// y -> (x1 -> x2) and (not x1 -> x3)
		clause.push(-y).push(-x1).push(x2);
		constrs[0] = processClause(clause);
		clause.clear();
		clause.push(-y).push(x1).push(x3);
		constrs[1] = processClause(clause);
		// y <- (x1 -> x2) and (not x1 -> x3)
		// not(x1 -> x2) or not(not x1 -> x3) or y
		// x1 and not x2 or not x1 and not x3 or y
		// (x1 and not x2) or ((not x1 or y) and (not x3 or y))
		// (x1 or not x1 or y) and (not x2 or not x1 or y) and (x1 or not x3 or
		// y) and (not x2 or not x3 or y)
		// not x1 or not x2 or y and x1 or not x3 or y and not x2 or not x3 or y
		clause.clear();
		clause.push(-x1).push(-x2).push(y);
		constrs[2] = processClause(clause);
		clause.clear();
		clause.push(x1).push(-x3).push(y);
		constrs[3] = processClause(clause);
		clause.clear();
		clause.push(-x2).push(-x3).push(y);
		constrs[4] = processClause(clause);
		// taken from Niklas Een et al SAT 2007 paper
		// Adding the following redundant clause will improve unit propagation
		// y -> x2 or x3
		clause.clear();
		clause.push(-y).push(x2).push(x3);
		constrs[5] = processClause(clause);
		return constrs;
	}

	/**
	 * Translate y <=> x1 /\ x2 /\ ... /\ xn into clauses.
	 *
	 * @param y
	 * @param literals
	 *            the x1 ... xn literals.
	 * @throws ContradictionException
	 * @since 2.1
	 */
	public IConstr[] and(int y, IVecInt literals) throws ContradictionException {
		// y <=> AND x1 ... xn
		IConstr[] constrs = new IConstr[literals.size() + 1];
		// y <= x1 .. xn
		IVecInt clause = new VecInt(literals.size() + 2);
		clause.push(y);
		for (int i = 0; i < literals.size(); i++) {
			clause.push(-literals.get(i));
		}
		constrs[0] = processClause(clause);
		clause.clear();
		for (int i = 0; i < literals.size(); i++) {
			// y => xi
			clause.clear();
			clause.push(-y);
			clause.push(literals.get(i));
			constrs[i + 1] = processClause(clause);
		}
		return constrs;
	}

	/**
	 * Translate y <=> x1 /\ x2
	 *
	 * @param y
	 * @param x1
	 * @param x2
	 * @throws ContradictionException
	 * @since 2.1
	 */
	public IConstr[] and(int y, int x1, int x2) throws ContradictionException {
		IVecInt clause = new VecInt(4);
		IConstr[] constrs = new IConstr[3];
		clause.push(-y);
		clause.push(x1);
		constrs[0] = addClause(clause);
		clause.clear();
		clause.push(-y);
		clause.push(x2);
		constrs[1] = addClause(clause);
		clause.clear();
		clause.push(y);
		clause.push(-x1);
		clause.push(-x2);
		constrs[2] = addClause(clause);
		return constrs;
	}

	/**
	 * translate y <=> x1 \/ x2 \/ ... \/ xn into clauses.
	 *
	 * @param y
	 * @param literals
	 * @throws ContradictionException
	 * @since 2.1
	 */
	public IConstr[] or(int y, IVecInt literals) throws ContradictionException {
		// y <=> OR x1 x2 ...xn
		// y => x1 x2 ... xn
		IConstr[] constrs = new IConstr[literals.size() + 1];
		IVecInt clause = new VecInt(literals.size() + 2);
		literals.copyTo(clause);
		clause.push(-y);
		constrs[0] = processClause(clause);
		clause.clear();
		for (int i = 0; i < literals.size(); i++) {
			// xi => y
			clause.clear();
			clause.push(y);
			clause.push(-literals.get(i));
			constrs[i + 1] = processClause(clause);
		}
		return constrs;
	}

	/**
	 * translate y <= x1 \/ x2 \/ ... \/ xn into clauses.
	 *
	 * @param y
	 * @param literals
	 * @throws ContradictionException
	 * @since 2.1
	 */
	public IConstr[] halfOr(int y, IVecInt literals)
			throws ContradictionException {
		IConstr[] constrs = new IConstr[literals.size()];
		IVecInt clause = new VecInt(literals.size() + 2);
		for (int i = 0; i < literals.size(); i++) {
			// xi => y
			clause.clear();
			clause.push(y);
			clause.push(-literals.get(i));
			constrs[i] = processClause(clause);
		}
		return constrs;
	}

	private IConstr processClause(IVecInt clause) throws ContradictionException {
		return addClause(clause);
	}

	/**
	 * Translate y <=> not x into clauses.
	 *
	 * @param y
	 * @param x
	 * @throws ContradictionException
	 * @since 2.1
	 */
	public IConstr[] not(int y, int x) throws ContradictionException {
		IConstr[] constrs = new IConstr[2];
		IVecInt clause = new VecInt(3);
		// y <=> not x
		// y => not x = not y or not x
		clause.push(-y).push(-x);
		constrs[0] = processClause(clause);
		// y <= not x = y or x
		clause.clear();
		clause.push(y).push(x);
		constrs[1] = processClause(clause);
		return constrs;
	}

	/**
	 * translate y <=> x1 xor x2 xor ... xor xn into clauses.
	 *
	 * @param y
	 * @param literals
	 * @throws ContradictionException
	 * @since 2.1
	 */
	public IConstr[] xor(int y, IVecInt literals) throws ContradictionException {
		literals.push(-y);
		int[] f = new int[literals.size()];
		literals.copyTo(f);
		IVec<IConstr> vconstrs = new Vec<IConstr>();
		xor2Clause(f, 0, false, vconstrs);
		IConstr[] constrs = new IConstr[vconstrs.size()];
		vconstrs.copyTo(constrs);
		return constrs;
	}

	/**
	 * translate y <=> (x1 <=> x2 <=> ... <=> xn) into clauses.
	 *
	 * @param y
	 * @param literals
	 * @throws ContradictionException
	 * @since 2.1
	 */
	public IConstr[] iff(int y, IVecInt literals) throws ContradictionException {
		literals.push(y);
		int[] f = new int[literals.size()];
		literals.copyTo(f);
		IVec<IConstr> vconstrs = new Vec<IConstr>();
		iff2Clause(f, 0, false, vconstrs);
		IConstr[] constrs = new IConstr[vconstrs.size()];
		vconstrs.copyTo(constrs);
		return constrs;
	}

	/**
	 * @since 2.2
	 */
	public void xor(int x, int a, int b) throws ContradictionException {
		IVecInt clause = new VecInt(3);
		clause.push(-a).push(b).push(x);
		processClause(clause);
		clause.clear();
		clause.push(a).push(-b).push(x);
		processClause(clause);
		clause.clear();
		clause.push(-a).push(-b).push(-x);
		processClause(clause);
		clause.clear();
		clause.push(a).push(b).push(-x);
		processClause(clause);
		clause.clear();
	}

	private void xor2Clause(int[] f, int prefix, boolean negation,
			IVec<IConstr> constrs) throws ContradictionException {
		if (prefix == f.length - 1) {
			IVecInt clause = new VecInt(f.length + 1);
			for (int i = 0; i < f.length - 1; ++i) {
				clause.push(f[i]);
			}
			clause.push(f[f.length - 1] * (negation ? -1 : 1));
			constrs.push(processClause(clause));
			return;
		}

		if (negation) {
			f[prefix] = -f[prefix];
			xor2Clause(f, prefix + 1, false, constrs);
			f[prefix] = -f[prefix];

			xor2Clause(f, prefix + 1, true, constrs);
		} else {
			xor2Clause(f, prefix + 1, false, constrs);

			f[prefix] = -f[prefix];
			xor2Clause(f, prefix + 1, true, constrs);
			f[prefix] = -f[prefix];
		}
	}

	private void iff2Clause(int[] f, int prefix, boolean negation,
			IVec<IConstr> constrs) throws ContradictionException {
		if (prefix == f.length - 1) {
			IVecInt clause = new VecInt(f.length + 1);
			for (int i = 0; i < f.length - 1; ++i) {
				clause.push(f[i]);
			}
			clause.push(f[f.length - 1] * (negation ? -1 : 1));
			processClause(clause);
			return;
		}

		if (negation) {
			iff2Clause(f, prefix + 1, false, constrs);
			f[prefix] = -f[prefix];
			iff2Clause(f, prefix + 1, true, constrs);
			f[prefix] = -f[prefix];
		} else {
			f[prefix] = -f[prefix];
			iff2Clause(f, prefix + 1, false, constrs);
			f[prefix] = -f[prefix];
			iff2Clause(f, prefix + 1, true, constrs);
		}
	}

	// From Een and Sorensson JSAT 2006 paper

	/**
	 * @since 2.2
	 */
	public void fullAdderSum(int x, int a, int b, int c)
			throws ContradictionException {
		IVecInt clause = new VecInt(4);
		// -a /\ -b /\ -c -> -x
		clause.push(a).push(b).push(c).push(-x);
		processClause(clause);
		clause.clear();
		// -a /\ b /\ c -> -x
		clause.push(a).push(-b).push(-c).push(-x);
		processClause(clause);
		clause.clear();
		clause.push(-a).push(b).push(-c).push(-x);
		processClause(clause);
		clause.clear();
		clause.push(-a).push(-b).push(c).push(-x);
		processClause(clause);
		clause.clear();
		clause.push(-a).push(-b).push(-c).push(x);
		processClause(clause);
		clause.clear();
		clause.push(-a).push(b).push(c).push(x);
		processClause(clause);
		clause.clear();
		clause.push(a).push(-b).push(c).push(x);
		processClause(clause);
		clause.clear();
		clause.push(a).push(b).push(-c).push(x);
		processClause(clause);
		clause.clear();
	}

	/**
	 * @since 2.2
	 */
	public void fullAdderCarry(int x, int a, int b, int c)
			throws ContradictionException {
		IVecInt clause = new VecInt(3);
		clause.push(-b).push(-c).push(x);
		processClause(clause);
		clause.clear();
		clause.push(-a).push(-c).push(x);
		processClause(clause);
		clause.clear();
		clause.push(-a).push(-b).push(x);
		processClause(clause);
		clause.clear();
		clause.push(b).push(c).push(-x);
		processClause(clause);
		clause.clear();
		clause.push(a).push(c).push(-x);
		processClause(clause);
		clause.clear();
		clause.push(a).push(b).push(-x);
		processClause(clause);
		clause.clear();
	}

	/**
	 * @since 2.2
	 */
	public void additionalFullAdderConstraints(int xcarry, int xsum, int a,
			int b, int c) throws ContradictionException {
		IVecInt clause = new VecInt(3);
		clause.push(-xcarry).push(-xsum).push(a);
		processClause(clause);
		clause.push(-xcarry).push(-xsum).push(b);
		processClause(clause);
		clause.push(-xcarry).push(-xsum).push(c);
		processClause(clause);
		clause.push(xcarry).push(xsum).push(-a);
		processClause(clause);
		clause.push(xcarry).push(xsum).push(-b);
		processClause(clause);
		clause.push(xcarry).push(xsum).push(-c);
		processClause(clause);
	}

	/**
	 * @since 2.2
	 */
	public void halfAdderSum(int x, int a, int b) throws ContradictionException {
		xor(x, a, b);
	}

	/**
	 * @since 2.2
	 */
	public void halfAdderCarry(int x, int a, int b)
			throws ContradictionException {
		and(x, a, b);
	}

	/**
	 * Translate an optimization function into constraints and provides the
	 * binary literals in results. Works only when the value of the objective
	 * function is positive.
	 *
	 * @since 2.2
	 */
	public void optimisationFunction(IVecInt literals, IVec<BigInteger> coefs,
			IVecInt result) throws ContradictionException {
		IVec<IVecInt> buckets = new Vec<IVecInt>();
		IVecInt bucket;
		// filling the buckets
		for (int i = 0; i < literals.size(); i++) {
			int p = literals.get(i);
			BigInteger a = coefs.get(i);
			for (int j = 0; j < a.bitLength(); j++) {
				bucket = createIfNull(buckets, j);
				if (a.testBit(j)) {
					bucket.push(p);
				}
			}
		}
		// creating the adder
		int x, y, z;
		int sum, carry;
		for (int i = 0; i < buckets.size(); i++) {
			bucket = buckets.get(i);
			while (bucket.size() >= 3) {
				x = bucket.get(0);
				y = bucket.get(1);
				z = bucket.get(2);
				bucket.remove(x);
				bucket.remove(y);
				bucket.remove(z);
				sum = nextFreeVarId(true);
				carry = nextFreeVarId(true);
				fullAdderSum(sum, x, y, z);
				fullAdderCarry(carry, x, y, z);
				additionalFullAdderConstraints(carry, sum, x, y, z);
				bucket.push(sum);
				createIfNull(buckets, i + 1).push(carry);
			}
			while (bucket.size() == 2) {
				x = bucket.get(0);
				y = bucket.get(1);
				bucket.remove(x);
				bucket.remove(y);
				sum = nextFreeVarId(true);
				carry = nextFreeVarId(true);
				halfAdderSum(sum, x, y);
				halfAdderCarry(carry, x, y);
				bucket.push(sum);
				createIfNull(buckets, i + 1).push(carry);
			}
			assert bucket.size() == 1;
			result.push(bucket.last());
			bucket.pop();
			assert bucket.isEmpty();
		}
	}

	/**
	 * Create a new bucket if it does not exists. Works only because the buckets
	 * are explored in increasing order.
	 *
	 * @param buckets
	 * @param i
	 * @return
	 */
	private IVecInt createIfNull(IVec<IVecInt> buckets, int i) {
		IVecInt bucket = buckets.get(i);
		if (bucket == null) {
			bucket = new VecInt();
			buckets.push(bucket);
			assert buckets.get(i) == bucket;
		}
		return bucket;

	}
}