/**
* Returns an automaton that accepts the concatenation of the languages of the given automata.
*
* <p>Complexity: linear in number of states.
*/
public static Automaton concatenate(Automaton a1, Automaton a2) {
if (a1.isSingleton() && a2.isSingleton())
return BasicAutomata.makeString(a1.singleton + a2.singleton);
if (isEmpty(a1) || isEmpty(a2)) return BasicAutomata.makeEmpty();
// adding epsilon transitions with the NFA concatenation algorithm
// in this case always produces a resulting DFA, preventing expensive
// redundant determinize() calls for this common case.
boolean deterministic = a1.isSingleton() && a2.isDeterministic();
if (a1 == a2) {
a1 = a1.cloneExpanded();
a2 = a2.cloneExpanded();
} else {
a1 = a1.cloneExpandedIfRequired();
a2 = a2.cloneExpandedIfRequired();
}
for (State s : a1.getAcceptStates()) {
s.accept = false;
s.addEpsilon(a2.initial);
}
a1.deterministic = deterministic;
// a1.clearHashCode();
a1.clearNumberedStates();
a1.checkMinimizeAlways();
return a1;
}
@Test
public void acceptViaRunning() {
State state = State.INITIAL;
state = state.run();
assertEquals(State.RUNNING, state);
state = state.accept();
assertEquals(State.ACCEPTED, state);
}
/**
* Returns a (deterministic) automaton that accepts the complement of the language of the given
* automaton.
*
* <p>Complexity: linear in number of states (if already deterministic).
*/
public static Automaton complement(Automaton a) {
a = a.cloneExpandedIfRequired();
a.determinize();
a.totalize();
for (State p : a.getNumberedStates()) p.accept = !p.accept;
a.removeDeadTransitions();
return a;
}
/** Returns a new (deterministic) automaton that accepts all strings. */
public static Automaton makeAnyString() {
Automaton a = new Automaton();
State s = new State();
a.initial = s;
s.accept = true;
s.transitions.add(new Transition(null, null, s));
a.deterministic = true;
return a;
}
/** Returns a new (deterministic) automaton that accepts all strings. */
public static DefaultAutomaton makeAnyString() {
DefaultAutomaton a = new DefaultAutomaton();
State s = new State();
a.initial = s;
s.accept = true;
s.transitions.add(new Transition(Character.MIN_VALUE, Character.MAX_VALUE, s));
a.deterministic = true;
return a;
}
/** Minimizes the given automaton using Huffman's algorithm. */
public static void minimizeHuffman(Automaton a) {
a.determinize();
a.totalize();
Set<State> ss = a.getStates();
Transition[][] transitions = new Transition[ss.size()][];
State[] states = ss.toArray(new State[ss.size()]);
boolean[][] mark = new boolean[states.length][states.length];
ArrayList<ArrayList<HashSet<IntPair>>> triggers = new ArrayList<ArrayList<HashSet<IntPair>>>();
for (int n1 = 0; n1 < states.length; n1++) {
ArrayList<HashSet<IntPair>> v = new ArrayList<HashSet<IntPair>>();
initialize(v, states.length);
triggers.add(v);
}
// initialize marks based on acceptance status and find transition arrays
for (int n1 = 0; n1 < states.length; n1++) {
states[n1].number = n1;
transitions[n1] = states[n1].getSortedTransitionArray(false);
for (int n2 = n1 + 1; n2 < states.length; n2++)
if (states[n1].accept != states[n2].accept) mark[n1][n2] = true;
}
// for all pairs, see if states agree
for (int n1 = 0; n1 < states.length; n1++)
for (int n2 = n1 + 1; n2 < states.length; n2++)
if (!mark[n1][n2]) {
if (statesAgree(transitions, mark, n1, n2)) addTriggers(transitions, triggers, n1, n2);
else markPair(mark, triggers, n1, n2);
}
// assign equivalence class numbers to states
int numclasses = 0;
for (int n = 0; n < states.length; n++) states[n].number = -1;
for (int n1 = 0; n1 < states.length; n1++)
if (states[n1].number == -1) {
states[n1].number = numclasses;
for (int n2 = n1 + 1; n2 < states.length; n2++)
if (!mark[n1][n2]) states[n2].number = numclasses;
numclasses++;
}
// make a new state for each equivalence class
State[] newstates = new State[numclasses];
for (int n = 0; n < numclasses; n++) newstates[n] = new State();
// select a class representative for each class and find the new initial
// state
for (int n = 0; n < states.length; n++) {
newstates[states[n].number].number = n;
if (states[n] == a.initial) a.initial = newstates[states[n].number];
}
// build transitions and set acceptance
for (int n = 0; n < numclasses; n++) {
State s = newstates[n];
s.accept = states[s.number].accept;
for (Transition t : states[s.number].transitions)
s.transitions.add(new Transition(t.min, t.max, newstates[t.to.number]));
}
a.removeDeadTransitions();
}
/**
* Returns a new (deterministic) automaton that accepts a single char whose value is in the given
* interval (including both end points).
*/
public static Automaton makeCharRange(Character min, Character max) {
if (min != null && max != null && min == max) return makeChar(min);
Automaton a = new Automaton();
State s1 = new State();
State s2 = new State();
a.initial = s1;
s2.accept = true;
if (min == null || max == null || min <= max) s1.transitions.add(new Transition(min, max, s2));
a.deterministic = true;
return a;
}
/**
* Returns a new (deterministic) automaton that accepts a single char whose value is in the given
* interval (including both end points).
*/
public static DefaultAutomaton makeCharRange(char min, char max) {
if (min == max) return makeChar(min);
DefaultAutomaton a = new DefaultAutomaton();
State s1 = new State();
State s2 = new State();
a.initial = s1;
s2.accept = true;
if (min <= max) s1.transitions.add(new Transition(min, max, s2));
a.deterministic = true;
return a;
}
/**
* Returns an automaton that accepts the union of the empty string and the language of the given
* automaton.
*
* <p>Complexity: linear in number of states.
*/
public static Automaton optional(Automaton a) {
a = a.cloneExpandedIfRequired();
State s = new State();
s.addEpsilon(a.initial);
s.accept = true;
a.initial = s;
a.deterministic = false;
// a.clearHashCode();
a.clearNumberedStates();
a.checkMinimizeAlways();
return a;
}
/** Returns a new (deterministic) automaton that accepts a single character in the given set. */
public static Automaton makeCharSet(String set) {
if (set.length() == 1) return makeChar(set.charAt(0));
Automaton a = new Automaton();
State s1 = new State();
State s2 = new State();
a.initial = s1;
s2.accept = true;
for (int i = 0; i < set.length(); i++) s1.transitions.add(new Transition(set.charAt(i), s2));
a.deterministic = true;
a.reduce();
return a;
}
/**
* Returns an automaton that accepts the Kleene star (zero or more concatenated repetitions) of
* the language of the given automaton. Never modifies the input automaton language.
*
* <p>Complexity: linear in number of states.
*/
public static Automaton repeat(Automaton a) {
a = a.cloneExpanded();
State s = new State();
s.accept = true;
s.addEpsilon(a.initial);
for (State p : a.getAcceptStates()) p.addEpsilon(s);
a.initial = s;
a.deterministic = false;
// a.clearHashCode();
a.clearNumberedStates();
a.checkMinimizeAlways();
return a;
}
/** Constructs deterministic automaton that matches strings that contain the given substring. */
public static DefaultAutomaton makeStringMatcher(String s) {
DefaultAutomaton a = new DefaultAutomaton();
State[] states = new State[s.length() + 1];
states[0] = a.initial;
for (int i = 0; i < s.length(); i++) states[i + 1] = new State();
State f = states[s.length()];
f.accept = true;
f.transitions.add(new Transition(Character.MIN_VALUE, Character.MAX_VALUE, f));
for (int i = 0; i < s.length(); i++) {
Set<Character> done = new HashSet<Character>();
char c = s.charAt(i);
states[i].transitions.add(new Transition(c, states[i + 1]));
done.add(c);
for (int j = i; j >= 1; j--) {
char d = s.charAt(j - 1);
if (!done.contains(d) && s.substring(0, j - 1).equals(s.substring(i - j + 1, i))) {
states[i].transitions.add(new Transition(d, states[j]));
done.add(d);
}
}
char[] da = new char[done.size()];
int h = 0;
for (char w : done) da[h++] = w;
Arrays.sort(da);
int from = Character.MIN_VALUE;
int k = 0;
while (from <= Character.MAX_VALUE) {
while (k < da.length && da[k] == from) {
k++;
from++;
}
if (from <= Character.MAX_VALUE) {
int to = Character.MAX_VALUE;
if (k < da.length) {
to = da[k] - 1;
k++;
}
states[i].transitions.add(new Transition((char) from, (char) to, states[0]));
from = to + 2;
}
}
}
a.deterministic = true;
return a;
}
/**
* Converts an incoming utf32 automaton to an equivalent utf8 one. The incoming automaton need not
* be deterministic. Note that the returned automaton will not in general be deterministic, so you
* must determinize it if that's needed.
*/
public Automaton convert(Automaton utf32) {
if (utf32.isSingleton()) {
utf32 = utf32.cloneExpanded();
}
State[] map = new State[utf32.getNumberedStates().length];
List<State> pending = new ArrayList<State>();
State utf32State = utf32.getInitialState();
pending.add(utf32State);
Automaton utf8 = new Automaton();
utf8.setDeterministic(false);
State utf8State = utf8.getInitialState();
utf8States = new State[5];
utf8StateCount = 0;
utf8State.number = utf8StateCount;
utf8States[utf8StateCount] = utf8State;
utf8StateCount++;
utf8State.setAccept(utf32State.isAccept());
map[utf32State.number] = utf8State;
while (pending.size() != 0) {
utf32State = pending.remove(pending.size() - 1);
utf8State = map[utf32State.number];
for (int i = 0; i < utf32State.numTransitions; i++) {
final Transition t = utf32State.transitionsArray[i];
final State destUTF32 = t.to;
State destUTF8 = map[destUTF32.number];
if (destUTF8 == null) {
destUTF8 = newUTF8State();
destUTF8.accept = destUTF32.accept;
map[destUTF32.number] = destUTF8;
pending.add(destUTF32);
}
convertOneEdge(utf8State, destUTF8, t.min, t.max);
}
}
utf8.setNumberedStates(utf8States, utf8StateCount);
return utf8;
}
/**
* Returns an automaton that accepts the concatenation of the languages of the given automata.
*
* <p>Complexity: linear in total number of states.
*/
public static Automaton concatenate(List<Automaton> l) {
if (l.isEmpty()) return BasicAutomata.makeEmptyString();
boolean all_singleton = true;
for (Automaton a : l)
if (!a.isSingleton()) {
all_singleton = false;
break;
}
if (all_singleton) {
StringBuilder b = new StringBuilder();
for (Automaton a : l) b.append(a.singleton);
return BasicAutomata.makeString(b.toString());
} else {
for (Automaton a : l) if (BasicOperations.isEmpty(a)) return BasicAutomata.makeEmpty();
Set<Integer> ids = new HashSet<Integer>();
for (Automaton a : l) ids.add(System.identityHashCode(a));
boolean has_aliases = ids.size() != l.size();
Automaton b = l.get(0);
if (has_aliases) b = b.cloneExpanded();
else b = b.cloneExpandedIfRequired();
Set<State> ac = b.getAcceptStates();
boolean first = true;
for (Automaton a : l)
if (first) first = false;
else {
if (a.isEmptyString()) continue;
Automaton aa = a;
if (has_aliases) aa = aa.cloneExpanded();
else aa = aa.cloneExpandedIfRequired();
Set<State> ns = aa.getAcceptStates();
for (State s : ac) {
s.accept = false;
s.addEpsilon(aa.initial);
if (s.accept) ns.add(s);
}
ac = ns;
}
b.deterministic = false;
// b.clearHashCode();
b.clearNumberedStates();
b.checkMinimizeAlways();
return b;
}
}
/**
* Simple, original brics implementation of determinize() Determinizes the given automaton using
* the given set of initial states.
*/
public static void determinizeSimple(Automaton a, Set<State> initialset) {
int[] points = a.getStartPoints();
// subset construction
Map<Set<State>, Set<State>> sets = new HashMap<Set<State>, Set<State>>();
LinkedList<Set<State>> worklist = new LinkedList<Set<State>>();
Map<Set<State>, State> newstate = new HashMap<Set<State>, State>();
sets.put(initialset, initialset);
worklist.add(initialset);
a.initial = new State();
newstate.put(initialset, a.initial);
while (worklist.size() > 0) {
Set<State> s = worklist.removeFirst();
State r = newstate.get(s);
for (State q : s)
if (q.accept) {
r.accept = true;
break;
}
for (int n = 0; n < points.length; n++) {
Set<State> p = new HashSet<State>();
for (State q : s)
for (Transition t : q.getTransitions())
if (t.min <= points[n] && points[n] <= t.max) p.add(t.to);
if (!sets.containsKey(p)) {
sets.put(p, p);
worklist.add(p);
newstate.put(p, new State());
}
State q = newstate.get(p);
int min = points[n];
int max;
if (n + 1 < points.length) max = points[n + 1] - 1;
else max = Character.MAX_CODE_POINT;
r.addTransition(new Transition(min, max, q));
}
}
a.deterministic = true;
a.clearNumberedStates();
a.removeDeadTransitions();
}
/** Minimizes the given automaton using Hopcroft's algorithm. */
public static void minimizeHopcroft(Automaton a) {
a.determinize();
Set<Transition> tr = a.initial.getTransitions();
if (tr.size() == 1) {
Transition t = tr.iterator().next();
if (t.to == a.initial && t.min == Transition.MIN_VALUE && t.max == Transition.MAX_VALUE)
return;
}
a.totalize();
// make arrays for numbered states and effective alphabet
Set<State> ss = a.getStates();
State[] states = new State[ss.size()];
int number = 0;
for (State q : ss) {
states[number] = q;
q.number = number++;
}
int[] sigma = a.getStartPoints();
// initialize data structures
ArrayList<ArrayList<LinkedList<State>>> reverse = new ArrayList<ArrayList<LinkedList<State>>>();
for (int q = 0; q < states.length; q++) {
ArrayList<LinkedList<State>> v = new ArrayList<LinkedList<State>>();
initialize(v, sigma.length);
reverse.add(v);
}
boolean[][] reverse_nonempty = new boolean[states.length][sigma.length];
ArrayList<LinkedList<State>> partition = new ArrayList<LinkedList<State>>();
initialize(partition, states.length);
int[] block = new int[states.length];
StateList[][] active = new StateList[states.length][sigma.length];
StateListNode[][] active2 = new StateListNode[states.length][sigma.length];
LinkedList<IntPair> pending = new LinkedList<IntPair>();
boolean[][] pending2 = new boolean[sigma.length][states.length];
ArrayList<State> split = new ArrayList<State>();
boolean[] split2 = new boolean[states.length];
ArrayList<Integer> refine = new ArrayList<Integer>();
boolean[] refine2 = new boolean[states.length];
ArrayList<ArrayList<State>> splitblock = new ArrayList<ArrayList<State>>();
initialize(splitblock, states.length);
for (int q = 0; q < states.length; q++) {
splitblock.set(q, new ArrayList<State>());
partition.set(q, new LinkedList<State>());
for (int x = 0; x < sigma.length; x++) {
reverse.get(q).set(x, new LinkedList<State>());
active[q][x] = new StateList();
}
}
// find initial partition and reverse edges
for (int q = 0; q < states.length; q++) {
State qq = states[q];
int j;
if (qq.accept) j = 0;
else j = 1;
partition.get(j).add(qq);
block[qq.number] = j;
for (int x = 0; x < sigma.length; x++) {
int y = sigma[x];
State p = qq.step(y);
reverse.get(p.number).get(x).add(qq);
reverse_nonempty[p.number][x] = true;
}
}
// initialize active sets
for (int j = 0; j <= 1; j++)
for (int x = 0; x < sigma.length; x++)
for (State qq : partition.get(j))
if (reverse_nonempty[qq.number][x]) active2[qq.number][x] = active[j][x].add(qq);
// initialize pending
for (int x = 0; x < sigma.length; x++) {
int a0 = active[0][x].size;
int a1 = active[1][x].size;
int j;
if (a0 <= a1) j = 0;
else j = 1;
pending.add(new IntPair(j, x));
pending2[x][j] = true;
}
// process pending until fixed point
int k = 2;
while (!pending.isEmpty()) {
IntPair ip = pending.removeFirst();
int p = ip.n1;
int x = ip.n2;
pending2[x][p] = false;
// find states that need to be split off their blocks
for (StateListNode m = active[p][x].first; m != null; m = m.next)
for (State s : reverse.get(m.q.number).get(x))
if (!split2[s.number]) {
split2[s.number] = true;
split.add(s);
int j = block[s.number];
splitblock.get(j).add(s);
if (!refine2[j]) {
refine2[j] = true;
refine.add(j);
}
}
// refine blocks
for (int j : refine) {
if (splitblock.get(j).size() < partition.get(j).size()) {
LinkedList<State> b1 = partition.get(j);
LinkedList<State> b2 = partition.get(k);
for (State s : splitblock.get(j)) {
b1.remove(s);
b2.add(s);
block[s.number] = k;
for (int c = 0; c < sigma.length; c++) {
StateListNode sn = active2[s.number][c];
if (sn != null && sn.sl == active[j][c]) {
sn.remove();
active2[s.number][c] = active[k][c].add(s);
}
}
}
// update pending
for (int c = 0; c < sigma.length; c++) {
int aj = active[j][c].size;
int ak = active[k][c].size;
if (!pending2[c][j] && 0 < aj && aj <= ak) {
pending2[c][j] = true;
pending.add(new IntPair(j, c));
} else {
pending2[c][k] = true;
pending.add(new IntPair(k, c));
}
}
k++;
}
for (State s : splitblock.get(j)) split2[s.number] = false;
refine2[j] = false;
splitblock.get(j).clear();
}
split.clear();
refine.clear();
}
// make a new state for each equivalence class, set initial state
State[] newstates = new State[k];
for (int n = 0; n < newstates.length; n++) {
State s = new State();
newstates[n] = s;
for (State q : partition.get(n)) {
if (q == a.initial) a.initial = s;
s.accept = q.accept;
s.number = q.number; // select representative
q.number = n;
}
}
// build transitions and set acceptance
for (int n = 0; n < newstates.length; n++) {
State s = newstates[n];
s.accept = states[s.number].accept;
for (Transition t : states[s.number].transitions)
s.transitions.add(new Transition(t.min, t.max, newstates[t.to.number]));
}
a.removeDeadTransitions();
}
/**
* Determinizes the given automaton.
*
* <p>Worst case complexity: exponential in number of states.
*/
static void determinize(Automaton a) {
if (a.deterministic || a.isSingleton()) {
return;
}
final State[] allStates = a.getNumberedStates();
// subset construction
final boolean initAccept = a.initial.accept;
final int initNumber = a.initial.number;
a.initial = new State();
SortedIntSet.FrozenIntSet initialset = new SortedIntSet.FrozenIntSet(initNumber, a.initial);
LinkedList<SortedIntSet.FrozenIntSet> worklist = new LinkedList<SortedIntSet.FrozenIntSet>();
Map<SortedIntSet.FrozenIntSet, State> newstate =
new HashMap<SortedIntSet.FrozenIntSet, State>();
worklist.add(initialset);
a.initial.accept = initAccept;
newstate.put(initialset, a.initial);
int newStateUpto = 0;
State[] newStatesArray = new State[5];
newStatesArray[newStateUpto] = a.initial;
a.initial.number = newStateUpto;
newStateUpto++;
// like Set<Integer,PointTransitions>
final PointTransitionSet points = new PointTransitionSet();
// like SortedMap<Integer,Integer>
final SortedIntSet statesSet = new SortedIntSet(5);
while (worklist.size() > 0) {
SortedIntSet.FrozenIntSet s = worklist.removeFirst();
// Collate all outgoing transitions by min/1+max:
for (int i = 0; i < s.values.length; i++) {
final State s0 = allStates[s.values[i]];
for (int j = 0; j < s0.numTransitions; j++) {
points.add(s0.transitionsArray[j]);
}
}
if (points.count == 0) {
// No outgoing transitions -- skip it
continue;
}
points.sort();
int lastPoint = -1;
int accCount = 0;
final State r = s.state;
for (int i = 0; i < points.count; i++) {
final int point = points.points[i].point;
if (statesSet.upto > 0) {
assert lastPoint != -1;
statesSet.computeHash();
State q = newstate.get(statesSet);
if (q == null) {
q = new State();
final SortedIntSet.FrozenIntSet p = statesSet.freeze(q);
worklist.add(p);
if (newStateUpto == newStatesArray.length) {
final State[] newArray =
new State
[ArrayUtil.oversize(1 + newStateUpto, RamUsageEstimator.NUM_BYTES_OBJ_REF)];
System.arraycopy(newStatesArray, 0, newArray, 0, newStateUpto);
newStatesArray = newArray;
}
newStatesArray[newStateUpto] = q;
q.number = newStateUpto;
newStateUpto++;
q.accept = accCount > 0;
newstate.put(p, q);
} else {
assert (accCount > 0 ? true : false) == q.accept
: "accCount="
+ accCount
+ " vs existing accept="
+ q.accept
+ " states="
+ statesSet;
}
r.addTransition(new Transition(lastPoint, point - 1, q));
}
// process transitions that end on this point
// (closes an overlapping interval)
Transition[] transitions = points.points[i].ends.transitions;
int limit = points.points[i].ends.count;
for (int j = 0; j < limit; j++) {
final Transition t = transitions[j];
final Integer num = t.to.number;
statesSet.decr(num);
accCount -= t.to.accept ? 1 : 0;
}
points.points[i].ends.count = 0;
// process transitions that start on this point
// (opens a new interval)
transitions = points.points[i].starts.transitions;
limit = points.points[i].starts.count;
for (int j = 0; j < limit; j++) {
final Transition t = transitions[j];
final Integer num = t.to.number;
statesSet.incr(num);
accCount += t.to.accept ? 1 : 0;
}
lastPoint = point;
points.points[i].starts.count = 0;
}
points.reset();
assert statesSet.upto == 0 : "upto=" + statesSet.upto;
}
a.deterministic = true;
a.setNumberedStates(newStatesArray, newStateUpto);
}
@Test
public void acceptImmediately() {
State state = State.INITIAL;
state = state.accept();
assertEquals(State.ACCEPTED, state);
}
/**
* Construct an NFA that will recognize a string matching this regular expression and then
* transition to a state that will accept with the given integer code.
*/
public State toNFA(int accept) {
State s = new State(); // Build a new state
s.accept = accept; // with specified accept code
s.trans = new Transition[0]; // and no outgoing transitions.
return this.toNFA(s); // Generate recognizer.
}
