// Returns true if there isn't a word that takes this state into a final ones
func (d *DFA) IsReverseUnreachable(state int) bool {
if d.IsFinal(state) {
return false
}
if len(d.Graph[state]) == 0 {
return true
}
q := queue.New(d.NumStates)
viz := make([]bool, d.NumStates+1)
q.Push(state)
for !q.Empty() {
node, _ := q.Pop()
for _, neighbours := range d.Graph[node] {
if viz[neighbours[0]] {
continue
}
if d.IsFinal(neighbours[0]) {
return false
}
viz[neighbours[0]] = true
q.Push(neighbours[0])
}
}
return true
}
func TestQ(t *testing.T) {
q := queue.New()
fmt.Println(q.Empty())
fmt.Println(q.Size())
fmt.Println("~~~~~~~~~~~")
for i := 0; i < 10; i++ {
q.Push(i)
fmt.Println(q.Empty())
fmt.Println(q.Size())
}
fmt.Println("~~~~~~~~~~~~~~")
for !q.Empty() {
fmt.Println(q.Front())
q.Pop()
}
}
// Transforms an NFA into a DFA that accepts the same language; some
// inaccessible states will be lost in the process
func (original_nfa *NFA) ToDFA() dfa.DFA {
nfa := Copy(*original_nfa)
n := &nfa
// first follow along λ-transitions to make them obsolete
is_final := make([]bool, n.NumStates+1)
for _, node := range n.FinalStates {
is_final[node] = true
}
for i := 1; i <= n.NumStates; i++ {
q := queue.New(n.NumStates)
added := make([]bool, n.NumStates+1)
for _, node := range n.Graph[i]['λ'] {
q.Push(node)
}
for !q.Empty() {
node, _ := q.Pop()
if is_final[node] && !is_final[i] {
is_final[i] = true
n.FinalStates = append(n.FinalStates, i)
}
for character, neighbours := range n.Graph[node] {
for _, neighbour := range neighbours {
if character == 'λ' && !added[neighbour] {
q.Push(neighbour)
added[neighbour] = true
}
n.Graph[i][character] = append(n.Graph[i][character], neighbour)
n.NumTransitions++
}
}
}
}
// then remove λ-transitions
for i := 1; i <= n.NumStates; i++ {
_, ok := n.Graph[i]['λ']
if ok {
n.NumTransitions -= len(n.Graph[i]['λ'])
delete(n.Graph[i], 'λ')
}
}
// then turn that into a DFA
visited := make([]bool, 1<<uint(n.NumStates+1))
dfa := make(map[int]map[rune]int)
q := queue.New(1 << uint(n.NumStates))
q.Push(1 << uint(n.EntryState-1))
final_states := make([]int, 0)
for !q.Empty() {
node_code, _ := q.Pop()
is_final_node := false
for node := 1; node < (1 << uint(n.NumStates)); node++ {
if 1<<uint(node-1) > node_code {
break
}
if ((1 << uint(node-1)) & node_code) == 0 {
continue
}
if is_final[node] {
is_final_node = true
}
if _, ok := dfa[node_code]; !ok {
dfa[node_code] = make(map[rune]int)
}
for character, neighbours := range n.Graph[node] {
for _, neighbour := range neighbours {
dfa[node_code][character] = dfa[node_code][character] | (1 << uint(neighbour-1))
}
}
for _, neighbour := range dfa[node_code] {
if !visited[neighbour] {
q.Push(neighbour)
visited[neighbour] = true
}
}
}
if is_final_node {
final_states = append(final_states, node_code)
}
}
// encode the newly created DFA into our standard form
for node, _ := range n.Graph {
delete(n.Graph, node)
}
nr := n.NumStates
n.NumStates = 0
n.NumTransitions = 0
n.EntryState = 1 << uint(n.EntryState-1)
mapping := make(map[int]int)
current_node := 0
for i := 1; i < (1 << uint(nr)); i++ {
if _, ok := dfa[i]; !ok || len(dfa[i]) == 0 {
continue
}
if _, ok := mapping[i]; !ok {
current_node++
mapping[i] = current_node
}
n.Graph[mapping[i]] = make(map[rune][]int)
n.NumTransitions += len(dfa[i])
for character, node := range dfa[i] {
if _, ok := mapping[node]; !ok {
current_node++
mapping[node] = current_node
}
n.Graph[mapping[i]][character] = []int{mapping[node]}
}
}
if _, ok := mapping[n.EntryState]; ok {
n.EntryState = mapping[n.EntryState]
} else {
current_node++
mapping[n.EntryState] = current_node
n.EntryState = current_node
}
n.NumStates = current_node
n.FinalStates = make([]int, 0)
for _, node := range final_states {
if _, ok := mapping[node]; ok {
n.FinalStates = append(n.FinalStates, mapping[node])
}
}
return n.DFA
}
// Minimize simplifies the DFA, by removing unnecessary states and merging
// states that can be merged
func (d *DFA) Minimize() {
// find unreachable and reverse-unreachable states
q := queue.New(d.NumStates)
to_remove := make([]bool, d.NumStates+1)
viz := make(map[int]bool)
nodes_removed := 0
transitions_removed := 0
q.Push(d.EntryState)
viz[d.EntryState] = true
for !q.Empty() {
node, _ := q.Pop()
for _, neighbours := range d.Graph[node] {
ok, _ := viz[neighbours[0]]
if !ok {
viz[neighbours[0]] = true
q.Push(neighbours[0])
}
}
}
for i := 1; i <= d.NumStates; i++ {
ok, _ := viz[i]
if !ok || d.IsReverseUnreachable(i) {
to_remove[i] = true
nodes_removed++
}
}
// Moore's Algorithm
// See http://en.wikipedia.org/wiki/DFA_minimization#Moore.27s_algorithm
is_final := make([]bool, d.NumStates+1)
renames := make(map[int]int)
for i := 1; i <= d.NumStates; i++ {
renames[i] = i
if d.IsFinal(i) {
is_final[i] = true
}
}
found_match := true
for found_match {
found_match = false
old_graph := d.Graph
for i := 1; i <= d.NumStates; i++ {
if to_remove[renames[i]] {
continue
}
for j := 1; j <= d.NumStates; j++ {
if to_remove[renames[i]] || renames[i] >= renames[j] {
continue
}
if is_final[renames[i]] && !is_final[renames[j]] ||
is_final[renames[j]] && !is_final[renames[i]] {
continue
}
match := nodes_match(old_graph, is_final, i, j)
if match {
// join states i and j
obsolete := 0
used := 0
if renames[i] > renames[j] {
obsolete, used = renames[i], renames[j]
renames[i] = renames[j]
} else {
obsolete, used = renames[j], renames[i]
renames[j] = renames[i]
}
if !to_remove[obsolete] {
to_remove[obsolete] = true
nodes_removed++
}
for character, nodes := range d.Graph[obsolete] {
if _, ok := d.Graph[used]; !ok {
d.Graph[used] = make(map[rune][]int)
}
if _, ok := d.Graph[used][character]; !ok {
d.Graph[used][character] = make([]int, 1)
} else {
transitions_removed++
}
d.Graph[used][character][0] = renames[nodes[0]]
}
renames[obsolete] = renames[used]
found_match = true
}
}
}
}
// Apply remaining renames
// TODO: improve the main algorithm so that it doesn't need this
for i := 1; i <= d.NumStates; i++ {
for character, _ := range d.Graph[i] {
for d.Graph[i][character][0] != renames[d.Graph[i][character][0]] {
d.Graph[i][character][0] = renames[d.Graph[i][character][0]]
}
}
}
for d.EntryState != renames[d.EntryState] {
d.EntryState = renames[d.EntryState]
}
// rename states so that there are no gaps between them
mapping := make(map[int]int)
next_available := 0
for node := 1; node <= d.NumStates; node++ {
if !to_remove[node] {
next_available++
mapping[node] = next_available
}
}
d.EntryState = mapping[d.EntryState]
final_states := make([]int, 0, len(d.FinalStates))
for id, _ := range d.FinalStates {
if _, ok := mapping[d.FinalStates[id]]; ok {
final_states = append(final_states, mapping[d.FinalStates[id]])
}
}
d.FinalStates = final_states
// rename the states found
for node, _ := range d.Graph {
for character, _ := range d.Graph[node] {
d.Graph[node][character][0] = mapping[d.Graph[node][character][0]]
}
}
for id := 1; id <= d.NumStates; id++ {
_, ok := mapping[id]
if !ok {
delete(d.Graph, id)
continue
}
d.Graph[mapping[id]] = d.Graph[id]
}
d.NumStates -= nodes_removed
d.NumTransitions -= transitions_removed
}
