def to_wfa(self):
trs = []
for _, tr_dest in self._trans.items():
for sym, dst in tr_dest.items():
if isinstance(dst, set):
for tr in dst:
trs.append(core_wfa.Transition(tr.src, tr.dest, \
tr.symbol, tr.weight))
else:
trs.append(core_wfa.Transition(dst.src, dst.dest, \
dst.symbol, dst.weight))
return core_wfa_export.CoreWFAExport(trs, self._fin, self._ini)
def _merge_states(self, partition):
"""Merge states according to a partition on a set of states and
create a new automaton.
Return: NFA (with merged states and modified transitions according
to a partitioning).
Keyword arguments:
partition -- Set([Frozenset([State])]) partitioning on a set of states.
"""
new_transitions = set([])
state_map = {}
for part in iter(partition):
for st in iter(part):
state_map[st] = part
for trans in self.get_transitions():
add_trans = core_wfa.Transition(state_map[trans.src], state_map[trans.dest], trans.symbol, trans.weight)
new_transitions.add(add_trans)
new_finals = {}
for key, _ in self.get_finals().iteritems():
new_finals[state_map[key]] = 1.0
new_initial = {}
ini = self.get_starts().keys()[0]
new_initial[state_map[ini]] = 1.0
return NFA(list(new_transitions), new_finals, new_initial, self.get_alphabet())
def _convert_to_pa(self, root, reduced=False):
self._pa = core_wfa_export.CoreWFAExport()
self._pa.set_starts({root: 1.0})
self._tree_to_pa(root, set([root]), reduced)
for pred, state in self._sinks.iteritems():
un_weight = 1.0 / (len(pred.symbols) + 1.0)
self._pa.get_finals()[state] = un_weight
for symbol in list(pred.symbols):
self._pa.get_transitions().append(
core_wfa.Transition(state, state, symbol, un_weight))
self._pa = self._pa.get_trim_automaton()
self._pa.__class__ = core_wfa_export.CoreWFAExport
def _create_path(self, root, pref, string):
if len(string) == 0:
root.value += 1
root.freq += 1
self._nodes[root] += 1
return
new = tree.Tree(0, {})
new.name = pref
self._nodes[new] = 0
trans = core_wfa.Transition(root, new, ord(string[0]), 1)
root.transitions[ord(string[0])] = trans
root.freq += 1
self._edges.append(trans)
self._create_path(new, pref + string[1:2], string[1:])
def get_dfa(self):
"""Get the deterministic version of the finite automaton. Implemented
using the powerset construction.
Return: NFA (but deterministic)
Note: States of the returned NFA are frozenset([State])
"""
initial = frozenset(super(NFA, self).get_starts().keys())
remaining = deque([initial])
completed = set()
finals = frozenset(super(NFA, self).get_finals().keys())
tr_dict = super(NFA, self).get_dictionary_transitions()
new_transitions = []
new_finals = dict()
state_dict_orig = dict()
for symbol in super(NFA, self).get_alphabet():
state_dict_orig[symbol] = set()
while remaining:
act = remaining.popleft()
completed.add(act)
if (act & finals) != frozenset():
new_finals[act] = 1.0
state_dict = copy.deepcopy(state_dict_orig)
for state in act:
for transition in tr_dict[state]:
state_dict[transition.symbol].add(transition.dest)
for symbol, state in state_dict.iteritems():
state = frozenset(state)
if state == frozenset():
continue
new_transitions.append(core_wfa.Transition(act, state, symbol, 1.0))
if (state not in completed) and (state not in remaining):
remaining.append(state)
return NFA(new_transitions, new_finals, {initial: 1.0}, super(NFA, self).get_alphabet())
def _tree_to_pa(self, node, visited, reduced):
if node.data != self._predicates.get_top():
return
if node.value > 0:
self._pa.get_finals()[node] = float(node.value) / node.freq
assert len(node.transitions) != 0, "TreeToPA -- incomplete tree"
for trans in node.transitions:
trans.weight = float(trans.weight) / trans.src.freq
if reduced and (trans.dest.data != self._predicates.get_top()):
self._pa.get_transitions().append(
core_wfa.Transition(trans.src,
self._sinks[trans.dest.data],
trans.symbol, trans.weight))
else:
self._pa.get_transitions().append(trans)
if trans.dest not in visited:
visited.add(trans.dest)
self._tree_to_pa(trans.dest, visited, reduced)
def add_selfloop(self, states):
"""Add self-loops containing all symbols from an alphabet to states
in states.
Keyword arguments:
states -- Set of states where the self-loops are added.
"""
alphabet = super(NFA, self).get_alphabet()
transitions = super(NFA, self).get_transitions()
finals = super(NFA, self).get_finals()
new_transitions = []
for transition in transitions:
if transition.src not in states:
new_transitions.append(transition)
for state in list(states):
for symbol in alphabet:
new_transitions.append(core_wfa.Transition(state, state, symbol, 1.0))
finals[state] = 1.0
super(NFA, self).set_transitions(new_transitions)
super(NFA, self).set_finals(finals)
def process_self_loop_state_approx(self, state, sparse=False):
"""Compute approximate state labels of the PA for a state state of the NFA.
It is assumed that the state state has self-loops (transitions from
predecessors are ignored).
Keyword arguments:
state -- State of the NFA.
"""
loop_transitions = []
lang_aggr = dict()
lang_weight = 0.0
for sym in self._nfa.get_alphabet():
loop_transitions.append(core_wfa.Transition(
state, state, sym, 1.0))
loop_nfa = nfa.NFA(loop_transitions, {state: 1.0}, {state: 1.0})
loop_nfa.rename_states()
pa_ini_states = self._reachable_states[state]
pa_copy = copy.copy(self._pa)
pa_copy.set_starts(pa_ini_states)
spa = pa_copy.product(loop_nfa)
spa = spa.get_trim_automaton()
spa.rename_states()
spa.__class__ = matrix_wfa.MatrixWFA
#Get initial and final vectors and compute the transition closure
closure = spa.compute_transition_closure(CLOSURE_MODE, sparse,
ITERATIONS)
wfa_wrap = WFAReachabilityWrap(spa, pa_copy.get_initial_vector(sparse),
spa.get_final_ones(sparse), closure)
lang_weight, lang_aggr = self._get_pa_states_reachability(
wfa_wrap, lang_aggr, lang_weight)
self._reachable_states[state] = lang_aggr
self._language_sum[state] = lang_weight
def _add_transitions(src, dest, symbols):
for sym in list(symbols):
src.transitions.append(core_wfa.Transition(src, dest, sym, 0))
def get_unambiguous_nfa(self, max_states=None):
"""Convert general NFA into UFA. Algorithm from article
Mohri: A Disambiguation Algorithm for Finite Automata and Functional
Transducers. The resulting UFA can be exponentialy more succinct than
input NFA.
Return instance of NFA.
"""
#TODO: Add support for multiple initial states
if len(super(NFA, self).get_starts()) != 1:
raise NFAOperationException("Only NFA with a single initial state can be converted unambiguous automaton.")
queue = deque([])
#queue = set([])
q_prime = set()
finals = super(NFA, self).get_finals().keys()
b = super(NFA, self).product(self)
b = b.get_trim_automaton()
b_states = b.get_states()
initial_state = super(NFA, self).get_starts().keys()[0]
s = frozenset([initial_state])
initial = (initial_state, s)
queue.append(initial)
q_prime.add(initial)
num_states = 1
finals_set = set([])
relation = set([(initial, initial)])
relation_dict = {}
relation_dict[initial] = set([initial])
new_transitions = set()
tr_dict = super(NFA, self).get_dictionary_transitions()
new_tr_dic = {}
while queue:
p, s = queue.popleft()
if p in finals:
is_final = True
for item in iter(relation_dict.get((p,s), [])): #aux.get_related(relation, (p, s)):
if item in finals_set:
is_final = False
break
if is_final:
finals_set.add((p, s))
for transition in tr_dict[p]:
delta = []
for state in list(s):
for state_tr in tr_dict[state]:
if state_tr.symbol == transition.symbol:
delta.append(state_tr.dest)
t_set = set()
for r in delta:
if (transition.dest, r) in b_states:
t_set.add(r)
t_set = frozenset(t_set)
cont = True
for item in iter(relation_dict.get((p,s), [])): #aux.get_related(relation, (p, s)):
if (item, transition.symbol, (transition.dest, t_set)) in new_transitions:
cont = False
break
if cont:
if (transition.dest, t_set) not in q_prime:
q_prime.add((transition.dest, t_set))
queue.append((transition.dest, t_set))
num_states += 1
if (max_states is not None) and (num_states > max_states):
return None
trans_item = ((p, s), transition.symbol, (transition.dest, t_set))
new_transitions.add(trans_item)
if trans_item[0] not in new_tr_dic:
new_tr_dic[trans_item[0]] = []
new_tr_dic[trans_item[0]].append(trans_item)
tmp = list(relation_dict.get((p,s), []))
for item in tmp: #aux.get_related(relation, (p, s)):
for tr_prime in new_tr_dic.get(item, []): #iter(new_transitions):
if (tr_prime[0] == item) and (tr_prime[1] == transition.symbol):
relation.add(((transition.dest, t_set), tr_prime[2]))
relation.add((tr_prime[2], (transition.dest, t_set)))
try:
relation_dict[tr_prime[2]].add((transition.dest, t_set))
except KeyError:
relation_dict[tr_prime[2]] = set([(transition.dest, t_set)])
try:
relation_dict[(transition.dest, t_set)].add(tr_prime[2])
except KeyError:
relation_dict[(transition.dest, t_set)] = set([tr_prime[2]])
transitions = []
finals = dict()
for item in list(new_transitions):
transitions.append(core_wfa.Transition(item[0], item[2], item[1], 1.0))
for fin in list(finals_set):
finals[fin] = 1.0
alphabet = self.get_alphabet()
return NFA(transitions, finals, {initial: 1.0}, alphabet)
