def concat(nfa1: NFA, nfa2: NFA):
nfa = NFA(Alphabet({Automata.EPSILON}))
equiv_states = {}
for state in nfa1.states:
equiv_states[state] = nfa.addState()
for state in nfa2.states:
equiv_states[state] = nfa.addState()
for start_state in nfa1.start:
nfa.start.add(equiv_states[start_state])
for final in nfa1.final:
for start in nfa2.start:
nfa.addTransition(equiv_states[final], equiv_states[start], NFA.EPSILON)
for state in nfa1.states:
for label in nfa.alphabet:
for dest in nfa1.transitions[state][label]:
nfa.addTransition(equiv_states[state], equiv_states[dest], label)
for state in nfa2.states:
for label in nfa.alphabet:
for dest in nfa2.transitions[state][label]:
nfa.addTransition(equiv_states[state], equiv_states[dest], label)
for final in nfa2.final:
nfa.final.add(equiv_states[final])
return nfa
def compile(db):
state = {}
res = NFA(-1)
res.add_transition(-1, NFA.ANY, -1)
for row in db:
res.add_transition(-1, NFA.EPSILON, (0,row))
for i,v in enumerate(row.sig):
v = (NFA.ANY,) if v is None else (chr(x) for x in v)
[res.add_transition((i,row), x, (i+1,row)) for x in v]
res.add_transition((i+1,row), NFA.ANY, (i+1,row))
res.add_final_state((i+1,row))
state.setdefault((i+1,row), []).append(row)
return state,res
def automata_concatenation(a1, a2):
c = {}
l = 0
d1 = 0
d2 = a1.states + d1
u = a2.states + d2
for (A, b), O in a1.map.items():
c[A + d1, b] = {F + d1 for F in O}
for (A, b), O in a2.map.items():
c[A + d2, b] = {F + d2 for F in O}
for z in a1.finals:
try:
X = c[z + d1, '']
except D:
X = c[z + d1, ''] = t()
X.add(a2.start + d2)
for z in a2.finals:
try:
X = c[z + d2, '']
except D:
X = c[z + d2, ''] = t()
X.add(u)
J = a1.states + a2.states + 2
S = {u}
return NFA(J, S, c, l)
def literal(literal: Literal):
nfa = NFA(Alphabet({Automata.EPSILON}))
start = nfa.addState()
final = nfa.addState()
nfa.start = {start}
nfa.final = {final}
for label in literal.alphabet:
for start in nfa.start:
for final in nfa.final:
nfa.addTransition(start, final, label)
return nfa
def automata_closure(a1):
c = {}
l = 0
d1 = 1
u = a1.states + d1
for (A, b), O in a1.map.items():
c[A + d1, b] = {F + d1 for F in O}
c[l, ''] = [a1.start + d1, u]
for z in a1.finals:
try:
X = c[z + d1, '']
except D:
X = c[z + d1, ''] = t()
X.add(u)
X.add(a1.start + d1)
J = a1.states + 2
S = {u}
return NFA(J, S, c, l)
def build_automaton_regular_grammar(G):
no_state = 0
states = {}
finals_states = []
transitions = {}
state_name = {}
for non_term in G.nonTerminals:
for prod in non_term.productions:
left, right = prod
try:
state_left = states[left]
except KeyError:
state_left = states[left] = no_state
state_name[no_state] = str(left)
no_state += 1
l = len(right)
if l == 1 or right == G.Epsilon:
new_state = no_state
state_name[no_state] = ' '
no_state += 1
finals_states.append(new_state)
try:
transitions[(state_left, str(right))].append(new_state)
except KeyError:
transitions[(state_left, str(right))] = [new_state]
elif l == 2:
nt = right._symbols[1]
try:
right_state = states[nt]
except KeyError:
right_state = states[nt] = no_state
state_name[no_state] = str(nt)
no_state += 1
try:
transitions[(state_left,
str(right._symbols[0]))].append(right_state)
except KeyError:
transitions[(state_left,
str(right._symbols[0]))] = [right_state]
nfa = NFA(no_state, finals_states, transitions, state_name,
states[G.startSymbol])
dfa = nfa_to_dfa(nfa)
return dfa
def automata_union(a1, a2):
c = {}
l = 0
d1 = 1
d2 = a1.states + d1
u = a2.states + d2
for (A, b), O in a1.map.items():
c[A + d1, b] = {F + d1 for F in O}
for (A, b), O in a2.map.items():
c[A + d2, b] = {F + d2 for F in O}
c[l, ''] = [a1.start + d1, a2.start + d2]
for dx, S in a([d1, d2], [a1.finals, a2.finals]):
for z in S:
try:
X = c[z + dx, '']
except D:
X = c[z + dx, ''] = t()
X.add(u)
J = a1.states + a2.states + 2
S = {u}
return NFA(J, S, c, l)
def __init__(self, states, finals, transitions, start=0):
assert L(y(value, e) for value in transitions.values())
assert L(g(b) > 0 for A, b in transitions)
transitions = {key: [value] for key, value in transitions.items()}
NFA.__init__(self, states, finals, transitions, start)
self.current = start
def evaluate(self):
s = self.lex
return NFA(states=2, finals=[1], transitions={(0, s): [1]})
def evaluate(self):
return NFA(states=1, finals=[0], transitions={})
def star(nfa: NFA):
new_start = nfa.addState()
new_end = nfa.addState()
for start in nfa.start:
nfa.addTransition(new_start, start, NFA.EPSILON)
for final in nfa.final:
nfa.addTransition(final, new_end, NFA.EPSILON)
for start in nfa.start:
for final in nfa.final:
nfa.addTransition(final, start, NFA.EPSILON)
nfa.addTransition(new_start, new_end, NFA.EPSILON)
nfa.start = [new_start]
nfa.final = [new_end]
return nfa
def emptyWord():
nfa = NFA(Alphabet())
nfa.start = {nfa.addState()}
nfa.final = nfa.start.copy()
return nfa
def union(nfa1: NFA, nfa2: NFA):
nfa = NFA(Alphabet({Automata.EPSILON}))
equiv_states = {}
for state in nfa1.states:
equiv_states[state] = nfa.addState()
for state in nfa2.states:
equiv_states[state] = nfa.addState()
for state in nfa1.states:
for label in nfa1.alphabet:
for dest in nfa1.transitions[state][label]:
nfa.addTransition(equiv_states[state], equiv_states[dest], label)
for state in nfa2.states:
for label in nfa2.alphabet:
for dest in nfa2.transitions[state][label]:
nfa.addTransition(equiv_states[state], equiv_states[dest], label)
new_start = nfa.addState()
new_end = nfa.addState()
for start in nfa1.start:
nfa.addTransition(new_start, equiv_states[start], NFA.EPSILON)
for start in nfa2.start:
nfa.addTransition(new_start, equiv_states[start], NFA.EPSILON)
for final in nfa1.final:
nfa.addTransition(equiv_states[final], new_end, NFA.EPSILON)
for final in nfa2.final:
nfa.addTransition(equiv_states[final], new_end, NFA.EPSILON)
nfa.start = {new_start}
nfa.final = {new_end}
return nfa
def compile(db):
state = {}
res = NFA(-1)
res.add_transition(-1, NFA.ANY, -1)
for row in db:
res.add_transition(-1, NFA.EPSILON, (0, row))
for i, v in enumerate(row.sig):
v = (NFA.ANY, ) if v is None else (chr(x) for x in v)
[res.add_transition((i, row), x, (i + 1, row)) for x in v]
res.add_transition((i + 1, row), NFA.ANY, (i + 1, row))
res.add_final_state((i + 1, row))
state.setdefault((i + 1, row), []).append(row)
return state, res