func newEmptyAutomaton() *Automaton {
return &Automaton{
deterministic: true,
curState: -1,
isAccept: util.NewOpenBitSet(),
}
}
// Minimizes the given automaton using Hopcroft's alforithm.
func minimizeHopcroft(a *Automaton) *Automaton {
if a.numStates() == 0 || !a.IsAccept(0) && a.numTransitions(0) == 0 {
// fastmatch for common case
return newEmptyAutomaton()
}
a = determinize(a)
if a.numTransitions(0) == 1 {
t := newTransition()
a.transition(0, 0, t)
if t.dest == 0 && t.min == MIN_CODE_POINT &&
t.max == unicode.MaxRune {
// accepts all strings
return a
}
}
a = totalize(a)
// initialize data structure
sigma := a.startPoints()
sigmaLen, statesLen := len(sigma), a.numStates()
reverse := make([][][]int, statesLen)
for i, _ := range reverse {
reverse[i] = make([][]int, sigmaLen)
}
partition := make([]map[int]bool, statesLen)
splitblock := make([][]int, statesLen)
block := make([]int, statesLen)
active := make([][]*StateList, statesLen)
for i, _ := range active {
active[i] = make([]*StateList, sigmaLen)
}
active2 := make([][]*StateListNode, statesLen)
for i, _ := range active2 {
active2[i] = make([]*StateListNode, sigmaLen)
}
pending := list.New()
pending2 := util.NewOpenBitSet() // sigmaLen * statesLen bits
split := util.NewOpenBitSet() // statesLen bits
refine := util.NewOpenBitSet() // statesLen bits
refine2 := util.NewOpenBitSet() // statesLen bits
for q, _ := range splitblock {
partition[q] = make(map[int]bool)
for x, _ := range active[q] {
active[q][x] = new(StateList)
}
}
// find initial partition and reverse edges
for q := 0; q < statesLen; q++ {
j := or(a.IsAccept(q), 0, 1).(int)
partition[j][q] = true
block[q] = j
for x, v := range sigma {
n := a.step(q, v)
assert2(n >= 0 && n < len(reverse), "%v", n)
r := reverse[a.step(q, v)]
r[x] = append(r[x], q)
}
}
// initialize active sets
for j := 0; j <= 1; j++ {
for x := 0; x < sigmaLen; x++ {
for q, _ := range partition[j] {
if reverse[q][x] != nil {
active2[q][x] = active[j][x].add(q)
}
}
}
}
// initialize pending
for x := 0; x < sigmaLen; x++ {
j := or(active[0][x].size <= active[1][x].size, 0, 1).(int)
pending.PushBack(&IntPair{j, x})
pending2.Set(int64(x*statesLen + j))
}
// process pending until fixed point
k := 2
// fmt.Println("start min")
for pending.Len() > 0 {
// fmt.Println(" cycle pending")
ip := pending.Remove(pending.Front()).(*IntPair)
p, x := ip.n1, ip.n2
// fmt.Printf(" pop n1=%v n2=%v\n", ip.n1, ip.n2)
pending2.Clear(int64(x*statesLen + p))
// find states that need to be split off their blocks
for m := active[p][x].first; m != nil; m = m.next {
if r := reverse[m.q][x]; r != nil {
for _, i := range r {
if !split.Get(int64(i)) {
split.Set(int64(i))
j := block[i]
splitblock[j] = append(splitblock[j], i)
if !refine2.Get(int64(j)) {
refine2.Set(int64(j))
refine.Set(int64(j))
}
}
}
}
}
// refine blocks
for j := int(refine.NextSetBit(0)); j >= 0; j = int(refine.NextSetBit(int64(j) + 1)) {
sb := splitblock[j]
if len(sb) < len(partition[j]) {
b1, b2 := partition[j], partition[k]
for _, s := range sb {
delete(b1, s)
b2[s] = true
block[s] = k
for c, sn := range active2[s] {
if sn != nil && sn.sl == active[j][c] {
sn.remove()
active2[s][c] = active[k][c].add(s)
}
}
}
// update pending
for c, _ := range active[j] {
aj := active[j][c].size
ak := active[k][c].size
ofs := int64(c * statesLen)
if !pending2.Get(ofs+int64(j)) && 0 < aj && aj <= ak {
pending2.Set(ofs + int64(j))
pending.PushBack(&IntPair{j, c})
} else {
pending2.Set(ofs + int64(k))
pending.PushBack(&IntPair{k, c})
}
}
k++
}
refine2.Clear(int64(j))
for _, s := range sb {
split.Clear(int64(s))
}
splitblock[j] = nil // clear sb
}
refine = util.NewOpenBitSet() // not quite efficient
}
ans := newEmptyAutomaton()
t := newTransition()
// fmt.Printf(" k=%v\n", k)
// make a new state for each equivalence class, set initial state
stateMap := make([]int, statesLen)
stateRep := make([]int, k)
ans.createState()
// fmt.Printf("min: k=%v\n", k)
for n := 0; n < k; n++ {
// fmt.Printf(" n=%v\n", n)
isInitial := false
for q, _ := range partition[n] {
if q == 0 {
isInitial = true
// fmt.Println(" isInitial!")
break
}
}
newState := 0
if !isInitial {
newState = ans.createState()
}
// fmt.Printf(" newState=%v\n", newState)
for q, _ := range partition[n] {
stateMap[q] = newState
// fmt.Printf(" q=%v isAccept?=%v\n", q, a.IsAccept(q))
ans.setAccept(newState, a.IsAccept(q))
stateRep[newState] = q // select representative
}
}
// build transitions and set acceptance
for n := 0; n < k; n++ {
numTransitions := a.initTransition(stateRep[n], t)
for i := 0; i < numTransitions; i++ {
a.nextTransition(t)
// fmt.Println(" add trans")
ans.addTransitionRange(n, stateMap[t.dest], t.min, t.max)
}
}
ans.finishState()
// fmt.Printf("%v states\n", ans.numStates())
return removeDeadStates(ans)
}
/*
Simple original brics implementation of determinize()
Determinizes the given automaton using the given set of initial states.
*/
func determinizeSimple(a *Automaton, initialset map[int]bool) *Automaton {
if a.numStates() == 0 {
return a
}
points := a.startPoints()
// subset construction
sets := make(map[string]bool)
hash := func(sets map[int]bool) string {
n := util.NewOpenBitSet()
for k, _ := range sets {
n.Set(int64(k))
}
return n.String()
}
worklist := list.New()
newstate := make(map[string]int)
sets[hash(initialset)] = true
worklist.PushBack(initialset)
b := newAutomatonBuilder()
b.createState()
newstate[hash(initialset)] = 0
t := newTransition()
for worklist.Len() > 0 {
s := worklist.Remove(worklist.Front()).(map[int]bool)
r := newstate[hash(s)]
for q, _ := range s {
if a.IsAccept(q) {
b.setAccept(r, true)
break
}
}
for n, point := range points {
p := make(map[int]bool)
for q, _ := range s {
count := a.initTransition(q, t)
for i := 0; i < count; i++ {
a.nextTransition(t)
if t.min <= point && point <= t.max {
p[t.dest] = true
}
}
}
hashKey := hash(p)
if _, ok := sets[hashKey]; !ok {
sets[hashKey] = true
worklist.PushBack(p)
newstate[hashKey] = b.createState()
}
q := newstate[hashKey]
min := point
var max int
if n+1 < len(points) {
max = points[n+1] - 1
} else {
max = unicode.MaxRune
}
b.addTransitionRange(r, q, min, max)
}
}
return removeDeadStates(b.finish())
}