/*
* Kodkod -- Copyright (c) 2005-present, Emina Torlak
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
package kodkod.engine.bool;
import static kodkod.engine.bool.BooleanConstant.FALSE;
import static kodkod.engine.bool.BooleanConstant.TRUE;
import static kodkod.engine.bool.Operator.AND;
import static kodkod.engine.bool.Operator.CONST;
import static kodkod.engine.bool.Operator.ITE;
import static kodkod.engine.bool.Operator.OR;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.ListIterator;
import kodkod.util.collections.CacheSet;
/**
* A factory for creating variables, binary gates, and if-then-else gates, in RBC form.
* @specfield values: set (BooleanVariable + MultiGate + ITEGate)
* @specfield cmpMax: int // the maximum number of comparisons made when comparing circuits for equality
* @invariant no disj factory, factory' : CircuitFactory | some factory.values & factory'.values
* @author Emina Torlak
*/
final class RBCFactory {
/**
* Stores input variables.
* @invariant all i: [1..iLits.size()] | vars[i-1].positive.label = i
*/
private final BooleanVariable[] vars;
/**
* Caches the AND, OR, and ITE gates.
* @invariant all i: [0..2] | c[i].op.ordinal = i
*/
private final CacheSet<BooleanFormula>[] cache;
private int label, cmpMax;
/**
* Constructs a CircuitFactory using the given max comparison parameter, initialized
* to contain the given number of variables.
* @requires cmpMax > 0 && numVars >= 0
* @ensures #this.values' = numVars && this.values in BooleanVariable
* @ensures this.cmpMax' = cmpMax
*/
@SuppressWarnings("unchecked") RBCFactory(int numVars, int cmpMax) {
assert cmpMax > 0 && numVars >= 0;
this.cmpMax = cmpMax;
this.label = numVars + 1;
vars = new BooleanVariable[numVars];
for(int i = 0; i < numVars; i++) {
vars[i]= new BooleanVariable(i+1);
}
cache = new CacheSet[]{new CacheSet<BooleanFormula>(), new CacheSet<BooleanFormula>(), new CacheSet<BooleanFormula>()};
}
/**
* Returns the cache for gates with the given operator.
* @requires op in AND + OR + ITE
* @return cache[op.ordinal]
*/
private CacheSet<BooleanFormula> opCache(Operator op) {
return cache[op.ordinal];
}
/**
* Sets this.cmpMax to the given value.
* @requires cmpMax > 0
* @ensures this.cmpMax' = cmpMax
*/
void setCmpMax(int cmpMax) {
assert cmpMax > 0;
this.cmpMax = cmpMax;
}
/**
* Returns this.cmpMax.
* @return this.cmpMax
*/
int cmpMax() { return cmpMax; }
/**
* Removes all MultiGates and ITEGates from this.factory.
* @ensures this.values' = this.values & BooleanVariable
*/
void clear() {
label = vars.length+1;
cache[0].clear();
cache[1].clear();
cache[2].clear();
}
/**
* Returns true if the given value
* is a valid argument to one of the <tt>assemble</tt>
* methods. Otherwise returns false.
* @return v in this.values + this.values.negation + BooleanConstant
*/
boolean canAssemble(BooleanValue v) {
if (v.op()==CONST) return true;
if (v.label() < 0) v = v.negation();
final int absLit = v.label();
if (absLit <= vars.length) {
return v == vars[absLit-1];
} else {
final BooleanFormula g = (BooleanFormula) v;
for(Iterator<BooleanFormula> gates = opCache(g.op()).get(g.hashCode()); gates.hasNext(); ) {
if (gates.next()==g) return true;
}
return false;
}
}
/**
* Returns the number of variables in this factory.
* @return #(this.values & BooleanVariable)
*/
int numVars() { return vars.length; }
/**
* Returns the boolean variable from this.values with the given label.
* @requires 0 < label <= #(this.values & BooleanVariable)
* @return (this.values & BooleanVariable).label
*/
BooleanVariable variable(int label) {
return vars[label-1];
}
/**
* Returns a boolean value whose meaning is (if [[i]] then [[t]] else [[e]]).
* @requires i + t + e in (this.values + this.values.negation + BooleanConstant)
* @return v: BooleanValue | [[v]] = if [[i]] then [[t]] else [[e]]
* @ensures v in BooleanFormula - NotGate => this.values' = this.values + v, this.values' = this.values
* @throws NullPointerException any of the arguments are null
*/
BooleanValue assemble(BooleanValue i, BooleanValue t, BooleanValue e) {
if (i==TRUE || t==e) return t;
else if (i==FALSE) return e;
else if (t==TRUE || i==t) return assemble(OR, i, e);
else if (t==FALSE || i.negation()==t) return assemble(AND, i.negation(), e);
else if (e==TRUE || i.negation()==e) return assemble(OR, i.negation(), t);
else if (e==FALSE || i==e) return assemble(AND, i, t);
else {
final int ilabel = i.label(), tlabel = t.label(), elabel = e.label();
boolean neg = false;
BooleanFormula f0 = (BooleanFormula) i, f1 = (BooleanFormula) t, f2 = (BooleanFormula) e;
if (Math.abs(tlabel)==Math.abs(elabel)) {
if (ilabel>0 && tlabel<0 && elabel>0) { // (a <=> !b) becomes !(a <=> b)
neg = true;
f1 = f1.negation();
f2 = f2.negation();
} else if (ilabel<0 && tlabel>0 && elabel<0) { // (!a <=> b) becomes !(a <=> b)
neg = true;
f0 = f0.negation();
} else if (ilabel<0 && tlabel<0 && elabel>0) {// (!a <=> !b) becomes (a <=> b)
f0 = f0.negation();
f1 = f1.negation();
f2 = f2.negation();
}
}
final int hash = ITE.hash(f0, f1, f2);
for(Iterator<BooleanFormula> gates = opCache(ITE).get(hash); gates.hasNext();) {
BooleanFormula gate = gates.next();
if (gate.input(0)==i && gate.input(1)==t && gate.input(2)==e)
return gate;
}
final BooleanFormula ret = new ITEGate(label++, hash, f0, f1, f2);
opCache(ITE).add(ret);
return neg ? ret.negation() : ret;
}
}
/**
* Returns a boolean value whose meaning is ([[v0]] op [[v1]]).
* @requires v0 + v1 in (this.values + this.values.negation + BooleanConstant)
* @return v: BooleanValue | [[v]] = [[v0]] op [[v1]]
* @ensures v in BooleanFormula - NotGate => this.values' = this.values + v, this.values' = this.values
* @throws NullPointerException any of the arguments are null
*/
BooleanValue assemble(Operator.Nary op, BooleanValue v0, BooleanValue v1) {
if (op==OR) {
return assemble(AND, v0.negation(), v1.negation()).negation();
}
if (v0==v1) return v0;
if (v0.label()==-v1.label()) return FALSE;
if (v0==TRUE) return v1;
if (v1==TRUE) return v0;
if (v0==FALSE) return FALSE;
if (v1==FALSE) return FALSE;
return cache(op, (BooleanFormula)v0, (BooleanFormula)v1);
}
/**
* Returns a boolean value with the same meaning as the given accumulator.
* @requires acc.components in (this.values + this.values.negation + BooleanConstant)
* @return v: BooleanValue | [[v]] = [[acc]]
* @ensures v in BooleanFormula - NotGate => this.values' = this.values + v, this.values' = this.values
* @throws NullPointerException any of the arguments are null
*/
BooleanValue assemble(BooleanAccumulator acc) {
final int asize = acc.size();
final Operator.Nary op = acc.op;
switch(asize) {
case 0 : return op.identity();
case 1 : return acc.iterator().next();
case 2 :
final Iterator<BooleanValue> inputs = acc.iterator();
return assemble(op, inputs.next(), inputs.next());
default :
final List<BooleanValue> vals = new LinkedList<BooleanValue>();
for(BooleanValue v : acc) {
vals.add(v);
}
while(vals.size()>1) {
final ListIterator<BooleanValue> itr = vals.listIterator();
for(int i = 0, max = vals.size()-1; i < max; i+=2) {
final BooleanValue v0 = itr.next();
itr.remove();
final BooleanValue v1 = itr.next();
final BooleanValue v0opv1 = assemble(op, v0, v1);
if (v0opv1==op.shortCircuit()) return op.shortCircuit();
else if (v0opv1==op.identity()) itr.remove();
else itr.set(v0opv1);
}
}
return vals.get(0);
}
}
/**
* Returns a BooleanFormula f such that [[f]] = f0 op f1. The method
* requires that the formulas f0 and f1 be already reduced with respect to op.
* A new formula is created and cached iff the circuit with the meaning
* [[f0]] op [[f1]] has not already been created.
* @requires f0 and f1 have already been reduced with respect to op; i.e.
* f0 op f1 cannot be reduced to a constant or a simple circuit
* by applying absorption, idempotence, etc. laws to f0 and f1.
* @return f : BooleanFormula | [[f]] = [[f0]] op [[f1]]
* @ensures f !in this.values => this.values' = this.values + f,
* this.values' = this.values
*/
private BooleanFormula cache(Operator.Nary op, BooleanFormula f0, BooleanFormula f1) {
final BooleanFormula l, h;
if (f0.label()<f1.label()) {
l = f0; h = f1;
} else {
l = f1; h = f0;
}
final int hash = op.hash(l,h);
for(Iterator<BooleanFormula> gates = opCache(op).get(hash); gates.hasNext(); ) {
BooleanFormula gate = gates.next();
if (gate.size()==2 && gate.input(0)==l && gate.input(1)==h)
return gate;
}
final BooleanFormula ret = new BinaryGate(op, label++, hash, l, h);
opCache(op).add(ret);
return ret;
}
}