package edu.stanford.nlp.fsm;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Set;
import edu.stanford.nlp.fsm.TransducerGraph.Arc;
import edu.stanford.nlp.util.Generics;
import edu.stanford.nlp.util.Maps;
import edu.stanford.nlp.util.Pair;
import edu.stanford.nlp.util.Timing;
/**
* Minimization of a FA in n log n a la Hopcroft.
*
* @author Dan Klein (klein@cs.stanford.edu)
*/
public class ExactAutomatonMinimizer implements AutomatonMinimizer {
private TransducerGraph unminimizedFA = null;
private Map<Arc, ExactBlock<Arc>> memberToBlock = null;
private LinkedList<Pair<ExactBlock<Arc>, Arc>> activePairs = null;
private boolean sparseMode = false;
private static final Arc SINK_NODE = new Arc(null);
protected TransducerGraph getUnminimizedFA() {
return unminimizedFA;
}
protected Collection<?> getSymbols() {
return getUnminimizedFA().getInputs();
}
public TransducerGraph minimizeFA(TransducerGraph unminimizedFA) {
this.unminimizedFA = unminimizedFA;
this.activePairs = Generics.newLinkedList();
this.memberToBlock = Generics.newHashMap();
minimize();
return buildMinimizedFA();
}
protected TransducerGraph buildMinimizedFA() {
TransducerGraph minimizedFA = new TransducerGraph();
TransducerGraph unminimizedFA = getUnminimizedFA();
for (TransducerGraph.Arc arc : unminimizedFA.getArcs()) {
Set<Arc> source = projectNode(arc.getSourceNode());
Set<Arc> target = projectNode(arc.getTargetNode());
try {
if (minimizedFA.canAddArc(source, target, arc.getInput(), arc.getOutput())) {
minimizedFA.addArc(source, target, arc.getInput(), arc.getOutput());
}
} catch (Exception e) {
//throw new IllegalArgumentException();
}
}
minimizedFA.setStartNode(projectNode(unminimizedFA.getStartNode()));
for (Object o : unminimizedFA.getEndNodes()) {
minimizedFA.setEndNode(projectNode(o));
}
return minimizedFA;
}
protected Set<Arc> projectNode(Object node) {
return getBlock(node).getMembers();
}
protected boolean hasActivePair() {
return activePairs.size() > 0;
}
protected Pair<ExactBlock<Arc>, ?> getActivePair() {
return activePairs.removeFirst();
}
protected void addActivePair(Pair<ExactBlock<Arc>, Arc> pair) {
activePairs.addLast(pair);
}
// protected Collection inverseImages(Collection block, Object symbol) {
// List inverseImages = new ArrayList();
// for (Iterator nodeI = block.iterator(); nodeI.hasNext();) {
// Object node = nodeI.next();
// inverseImages.addAll(getUnminimizedFA().getInboundArcs(node, symbol));
// }
// return inverseImages;
// }
protected <Y> Map<ExactBlock<Arc>, Set<Y>> sortIntoBlocks(Collection<Y> nodes) {
Map<ExactBlock<Arc>, Set<Y>> blockToMembers = Generics.newHashMap(); // IdentityHashMap();
for (Y o : nodes) {
ExactBlock<Arc> block = getBlock(o);
if (block == null) {
throw new RuntimeException("got null block");
}
Maps.putIntoValueHashSet(blockToMembers, block, o);
}
return blockToMembers;
}
protected void makeBlock(Collection<Arc> members) {
ExactBlock<Arc> block = new ExactBlock<>(Generics.newHashSet(members));
for (Arc member : block.getMembers()) {
if (member != SINK_NODE) {
memberToBlock.put(member, block);
}
}
for (Object o : getSymbols()) {
Arc symbol = (Arc) o;
addActivePair(new Pair<>(block, symbol));
}
}
protected static void removeAll(Collection<? extends Arc> block, Collection members) {
// this is because AbstractCollection/Set.removeAll() isn't always linear in members.size()
for (Object member : members) {
block.remove(member);
}
}
protected static Collection<Arc> difference(Collection<Arc> block, Collection<Arc> members) {
Set<Arc> difference = Generics.newHashSet();
for (Arc member : block) {
if (!members.contains(member)) {
difference.add(member);
}
}
return difference;
}
protected ExactBlock<Arc> getBlock(Object o) {
ExactBlock<Arc> result = memberToBlock.get(o);
if (result == null) {
throw new RuntimeException("memberToBlock had null block");
}
return result;
}
protected Collection<Object> getInverseImages(ExactBlock<Arc> block, Object symbol) {
List<Object> inverseImages = new ArrayList<>();
for (Arc member : block.getMembers()) {
Collection<Arc> arcs = null;
if (member != SINK_NODE) {
arcs = getUnminimizedFA().getArcsByTargetAndInput(member, symbol);
} else {
arcs = getUnminimizedFA().getArcsByInput(symbol);
if (!sparseMode) {
arcs = difference(getUnminimizedFA().getArcs(), arcs);
}
}
if (arcs == null) {
continue;
}
for (Arc arc : arcs) {
Object source = arc.getSourceNode();
inverseImages.add(source);
}
}
return inverseImages;
}
protected void makeInitialBlocks() {
// sink block (for if the automaton isn't complete
makeBlock(Collections.singleton(SINK_NODE));
// accepting block
Set<Arc> endNodes = getUnminimizedFA().getEndNodes();
makeBlock(endNodes);
// main block
Collection<Arc> nonFinalNodes = Generics.newHashSet(getUnminimizedFA().getNodes());
nonFinalNodes.removeAll(endNodes);
makeBlock(nonFinalNodes);
}
protected void minimize() {
makeInitialBlocks();
while (hasActivePair()) {
Pair<ExactBlock<Arc>, ?> activePair = getActivePair();
ExactBlock<Arc> activeBlock = activePair.first();
Object symbol = activePair.second();
Collection<Object> inverseImages = getInverseImages(activeBlock, symbol);
Map<ExactBlock<Arc>, Set<Object>> inverseImagesByBlock = sortIntoBlocks(inverseImages);
for (ExactBlock<Arc> block : inverseImagesByBlock.keySet()) {
if (block == null) {
throw new RuntimeException("block was null");
}
Collection members = inverseImagesByBlock.get(block);
if (members.size() == 0 || members.size() == block.getMembers().size()) {
continue;
}
if (members.size() > block.getMembers().size() - members.size()) {
members = difference(block.getMembers(), members);
}
removeAll(block.getMembers(), members);
makeBlock(members);
}
}
}
public ExactAutomatonMinimizer(boolean sparseMode) {
this.sparseMode = sparseMode;
}
public ExactAutomatonMinimizer() {
this(false);
}
private static class ExactBlock<E> implements Block<E> {
private final Set<E> members;
public Set<E> getMembers() {
return members;
}
public ExactBlock(Set<E> members) {
if (members == null) {
throw new IllegalArgumentException("tried to create block with null members.");
}
this.members = members;
}
@Override
public String toString() {
return "Block: " + members.toString();
}
} // end static class ExactBlock
public static void main(String[] args) {
TransducerGraph fa = new TransducerGraph();
fa.addArc(fa.getStartNode(), "1", "a", "");
fa.addArc(fa.getStartNode(), "2", "b", "");
fa.addArc(fa.getStartNode(), "3", "c", "");
fa.addArc("1", "4", "a", "");
fa.addArc("2", "4", "a", "");
fa.addArc("3", "5", "c", "");
fa.addArc("4", "6", "c", "");
fa.addArc("5", "6", "c", "");
fa.setEndNode("6");
System.out.println(fa);
ExactAutomatonMinimizer minimizer = new ExactAutomatonMinimizer();
System.out.println(minimizer.minimizeFA(fa));
System.out.println("Starting...");
Timing.startTime();
TransducerGraph randomFA = TransducerGraph.createRandomGraph(100, 10, 1.0, 10, new ArrayList());
TransducerGraph minimizedRandomFA = minimizer.minimizeFA(randomFA);
System.out.println(randomFA);
System.out.println(minimizedRandomFA);
Timing.tick("done. ( " + randomFA.getArcs().size() + " arcs to " + minimizedRandomFA.getArcs().size() + " arcs)");
}
}