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Open-source constraint solver.
/*
* This file is part of choco-solver, http://choco-solver.org/
*
* Copyright (c) 2022, IMT Atlantique. All rights reserved.
*
* Licensed under the BSD 4-clause license.
*
* See LICENSE file in the project root for full license information.
*/
package org.chocosolver.solver.constraints.nary.cnf;
import org.chocosolver.solver.Model;
import org.chocosolver.solver.variables.BoolVar;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
/**
* A tool box to convert logical expressions into CNF.
*
*
* @author Charles Prud'homme, Xavier Lorca
* @since 23 nov. 2010
*/
public class LogicTreeToolBox {
/**
* This class is a factory, no need to create it.
*/
protected LogicTreeToolBox() {
}
/**
* Warning: if there is a bug, please check the CNF build is like:
* - lit OR lit ... OR lit
* - (lit OR lit ... OR lit) AND (lit OR lit ... OR lit) ... AND (lit OR lit ... OR lit)
*
* @param logOp logical operator
* @param model the model in which the logical expression will be added, useful since the expression may only be made of TRUE and FALSE.
* @return a CNF logical expression
*/
public static ILogical toCNF(LogOp logOp, Model model) {
expandNot(logOp);
logOp = distribute(logOp);
// sort children of each clause with positive literals first
if (logOp.is(LogOp.Operator.OR)) {
sort(logOp);
}
ILogical[] children = logOp.getChildren();
for (int i = 0; i < children.length; i++) {
if (!children[i].isLit()) {
LogOp nc = (LogOp) children[i];
if (nc.is(LogOp.Operator.OR)) {
sort(nc);
}
}
}
ILogical l = simplify(logOp, model);
l = simplifySingleton(l, model);
l = orderAndReduce(l);
if (!l.isLit()) ((LogOp) l).cleanFlattenBoolVar();
return l;
}
/**
* Erases 'NOT' operand from the logical expression n by flipping the right children
* @param n a logical expression
*/
public static void expandNot(LogOp n) {
if (n.isNot()) {
n.flip();
}
ILogical[] children = n.getChildren();
for (int i = 0; i < children.length; i++) {
if (!children[i].isLit()) {
expandNot((LogOp) children[i]);
}
}
}
/**
* Flattens a logical expression n based on operator op.
* Transform from undefined depth expression to comb expression
* @param op reference operator
* @param n the lofical expression
*/
public static void merge(LogOp.Operator op, LogOp n) {
if (n.is(op)) {
ILogical[] children = n.getChildren();
for (int i = 0; i < children.length; i++) {
ILogical child = children[i];
if (!child.isLit()) {
LogOp nc = (LogOp) child;
if (nc.is(op)) {
merge(op, nc);
ILogical[] subchildren = nc.getChildren();
n.removeChild(child);
for (int j = 0; j < subchildren.length; j++) {
n.addChild(subchildren[j]);
}
}
}
}
}
}
/**
* Moves down 'OR' operand in the logical expression n.
* @param n a logical expression
* @return the modified logical expression
*/
@SuppressWarnings("ConstantConditions")
public static LogOp developOr(LogOp n) {
ILogical t1 = n.getAndChild();
ILogical t2 = n.getChildBut(t1);
LogOp tt = LogOp.and();
if (!(t1 != null && t1.isLit())) {
LogOp n1 = (LogOp) t1;
ILogical[] t1cs = n1.getChildren();
for (int i = 0; i < t1cs.length; i++) {
ILogical t1c = t1cs[i];
if (t2 != null) {
if (t2.isLit()) {
tt.addChild(LogOp.or(t1c, t2));
} else {
ILogical[] t2cs = ((LogOp) t2).getChildren();
for (int j = 0; j < t2cs.length; j++) {
ILogical t2c = t2cs[j];
tt.addChild(LogOp.or(t1c, t2c));
}
}
}
}
}
n.removeChild(t1);
n.removeChild(t2);
if (n.getNbChildren() == 0) {
return tt;
} else {
n.addChild(tt);
return n;
}
}
/**
* Distributes 'OR's inwards over 'AND's in n
* @param n a logical expression
* @return the modified logical expression
*/
public static LogOp distribute(LogOp n) {
if (n.is(LogOp.Operator.AND)) {
ILogical[] children = n.getChildren();
for (int i = 0; i < children.length; i++) {
if (!children[i].isLit()) {
children[i] = distribute((LogOp) children[i]);
}
}
} else {
if (n.hasOrChild()) {
merge(LogOp.Operator.OR, n);
}
if (n.hasAndChild() && n.getNbChildren() > 1) {
n = distribute(developOr(n));
}
}
merge(LogOp.Operator.AND, n);
return n;
}
/**
* Extracts the array of {@link BoolVar} from node
* @param node a logical expression
* @return the array of {@link BoolVar} from node
*/
private static BoolVar[] extract(ILogical node) {
if (node.isLit()) {
return new BoolVar[]{(BoolVar) node};
} else {
return ((LogOp) node).flattenBoolVar();
}
}
/**
* Detects tautologies and contradictions from t
* @param t a logical expression
* @param model to get {@link Model#boolVar(boolean)}.
* @return simplified logical expression
*/
public static ILogical simplify(ILogical t, Model model) {
if (t.isLit()) return t;
// else
LogOp n = (LogOp) t;
ILogical[] children = n.getChildren();
if (n.is(LogOp.Operator.OR)) {
// OR with only LITS
HashMap lits = new HashMap<>();
for (int i = 0; i < children.length; i++) {
BoolVar var = extract(children[i])[0];
var = var.isNot() ? var.not() : var;
if (lits.containsKey(var)) {
ILogical prev = lits.get(var);
if (prev.isNot() != children[i].isNot()) {
return model.boolVar(true);
}
} else {
lits.put(var, children[i]);
}
}
ILogical[] ts = lits.values().toArray(new ILogical[0]);
// Arrays.sort(ts);
return LogOp.or(ts);
} else if (!n.hasOrChild()) {
// AND with only LITS
HashMap lits = new HashMap<>();
for (int i = 0; i < children.length; i++) {
BoolVar var = extract(children[i])[0];
var = var.isNot() ? var.not() : var;
if (lits.containsKey(var)) {
ILogical prev = lits.get(var);
if (prev.isNot() != children[i].isNot()) {
return model.boolVar(false);
}
} else {
lits.put(var, children[i]);
}
}
ILogical[] ts = lits.values().toArray(new ILogical[0]);
// Arrays.sort(ts);
return LogOp.and(ts);
} else {
for (int i = 0; i < children.length; i++) {
if (!children[i].isLit()) {
children[i] = simplify(children[i], model);
}
}
}
return t;
}
/**
* Remove tautologies from l
* @param l logical expression
* @param model to get {@link Model#intVar(int)}.
* @return simplified logical expression
*/
public static ILogical simplifySingleton(ILogical l, Model model) {
if (l.isLit()) return l;
LogOp t = (LogOp) l;
ILogical[] children = t.getChildren();
ArrayList toRemove = new ArrayList<>();
for (int i = 0; i < children.length; i++) {
if (model.boolVar(true).equals(children[i])) {
toRemove.add(children[i]);
}
}
toRemove.forEach(t::removeChild);
if (t.getNbChildren() == 1) {
return t.getChildren()[0];
}
return t;
}
/**
* Reorder l in order to eliminate duplicates
* @param t the logical expression to order and reduce
* @return reordered logical expression
*/
private static ILogical orderAndReduce(ILogical t) {
if (t.isLit()) return t;
LogOp n = (LogOp) t;
ILogical[] children = n.getChildren();
for (int i = 0; i < children.length; i++) {
if (!children[i].isLit()) {
Arrays.sort(((LogOp)children[i]).getChildren(), LogicTreeToolBox::sameLogical);
}
}
Arrays.sort(children, LogicTreeToolBox::sameLogical);
int i = 0;
int k = children.length-1;
while(i < k ){
if(sameLogical(children[i], children[i+1]) == 0){
System.arraycopy(children, i+1, children, i, children.length - i - 1);
k--;
}else {
i++;
}
}
if(k == 0){
return children[0];
}else {
return new LogOp(n.operator, n.type, Arrays.copyOf(children, k + 1));
}
}
/**
* Sort a logical expression wrt to NOT
* @param logOp logical expression to sort
*/
private static void sort(LogOp logOp){
Arrays.sort(logOp.getChildren(), (o1, o2) -> {
if (o1.isNot() == o2.isNot()) {
return 0;
} else if (o2.isNot()) {
return -1;
}
return 1;
});
}
private static int sameLogical(ILogical o1, ILogical o2){
if (o1.isLit()) {
if (o2.isLit()) {
return sameLit(o1, o2);
} else {
return -1;
}
} else {
if (o2.isLit()) {
return 1;
} else {
LogOp l1 = (LogOp)o1;
LogOp l2 = (LogOp)o2;
return sameChild(l1, l2);
}
}
}
private static int sameLit(ILogical o1, ILogical o2){
int diff = ((BoolVar) o1).getId() - ((BoolVar) o2).getId();
if(diff == 0){
if (o1.isNot() == o2.isNot()) {
return 0;
} else if (o2.isNot()) {
return -1;
}
return 1;
}else {
return diff;
}
}
private static int sameChild(LogOp l1, LogOp l2){
if(l1.getNbChildren() == l2.getNbChildren()){
// assume l1 and l2 are already sorted
int i = 0;
int same = 0;
ILogical ll1, ll2;
while(i < l1.getNbChildren() && same == 0){
ll1 = l1.getChildren()[i];
ll2 = l2.getChildren()[i];
assert ll1.isLit();
assert ll2.isLit();
same = sameLit(ll1, ll2);
i++;
}
return same;
}else{
return l1.getNbChildren() - l2.getNbChildren();
}
}
}