/** 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;
}
/**
* Constructs sub-automaton corresponding to decimal numbers of value at most x.substring(n) and
* length x.substring(n).length().
*/
private static State atMost(String x, int n) {
State s = new State();
if (x.length() == n) s.setAccept(true);
else {
char c = x.charAt(n);
s.addTransition(new Transition(c, atMost(x, (char) n + 1)));
if (c > '0') s.addTransition(new Transition('0', (char) (c - 1), anyOfRightLength(x, n + 1)));
}
return s;
}
/** Minimizes the given automaton using Huffman's algorithm. */
public static void minimizeHuffman(LinkedAutomaton a) {
determinize(a);
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 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;
}
/**
* Constructs sub-automaton corresponding to decimal numbers of value at least x.substring(n) and
* length x.substring(n).length().
*/
private static State atLeast(String x, int n, Collection<State> initials, boolean zeros) {
State s = new State();
if (x.length() == n) s.setAccept(true);
else {
if (zeros) initials.add(s);
char c = x.charAt(n);
s.addTransition(new Transition(c, atLeast(x, n + 1, initials, zeros && c == '0')));
if (c < '9') s.addTransition(new Transition((char) (c + 1), '9', anyOfRightLength(x, n + 1)));
}
return s;
}
/** Returns a new (deterministic) automaton that accepts a single character in the given set. */
public static DefaultAutomaton makeCharSet(String set) {
if (set.length() == 1) return makeChar(set.charAt(0));
DefaultAutomaton a = new DefaultAutomaton();
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;
}
/** 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;
}
/**
* Constructs sub-automaton corresponding to decimal numbers of value between x.substring(n) and
* y.substring(n) and of length x.substring(n).length() (which must be equal to
* y.substring(n).length()).
*/
private static State between(
String x, String y, int n, Collection<State> initials, boolean zeros) {
State s = new State();
if (x.length() == n) s.setAccept(true);
else {
if (zeros) initials.add(s);
char cx = x.charAt(n);
char cy = y.charAt(n);
if (cx == cy)
s.addTransition(new Transition(cx, between(x, y, n + 1, initials, zeros && cx == '0')));
else { // cx<cy
s.addTransition(new Transition(cx, atLeast(x, n + 1, initials, zeros && cx == '0')));
s.addTransition(new Transition(cy, atMost(y, n + 1)));
if (cx + 1 < cy)
s.addTransition(
new Transition((char) (cx + 1), (char) (cy - 1), anyOfRightLength(x, n + 1)));
}
}
return s;
}
/** Minimizes the given automaton using Hopcroft's algorithm. */
public static void minimizeHopcroft(LinkedAutomaton a) {
determinize(a);
Set<Transition> tr = a.initial.getTransitions();
if (tr.size() == 1) {
Transition t = tr.iterator().next();
if (t.to == a.initial && t.min == Character.MIN_VALUE && t.max == Character.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++;
}
char[] 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 != null) j = 0;
else j = 1;
partition.get(j).add(qq);
block[qq.number] = j;
for (int x = 0; x < sigma.length; x++) {
char 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();
}
/**
* Constructs sub-automaton corresponding to decimal numbers of length x.substring(n).length().
*/
private static State anyOfRightLength(String x, int n) {
State s = new State();
if (x.length() == n) s.setAccept(true);
else s.addTransition(new Transition('0', '9', anyOfRightLength(x, n + 1)));
return s;
}