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dc_dfa.py
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import numpy as np
from aalpy.base import Automaton
from aalpy.automata.Dfa import Dfa, DfaState
from aalpy.automata.MealyMachine import MealyMachine, MealyState
from itertools import combinations
def dfa3_to_tables(dfa3: Automaton):
output_map = {"-": 0, "+": 1, "?": 2}
alphabet = dfa3.get_input_alphabet()
transitions = np.zeros((dfa3.size, len(alphabet)), dtype=int)
outputs = np.zeros((dfa3.size, len(alphabet)), dtype=int)
state_to_idx = dict()
idx_to_state = dict()
for i, s in enumerate(dfa3.states):
state_to_idx[s] = i
idx_to_state[i] = s
for i, s in enumerate(dfa3.states):
for j, a in enumerate(alphabet):
next = s.transitions[a]
transitions[i, j] = state_to_idx[next]
outputs[i, j] = output_map[next.output]
return transitions, outputs, state_to_idx[dfa3.initial_state]
def is_pair_aligned(i,j, outputs):
return np.all((outputs[i, :] == 2) | (outputs[j, :] == 2) | (outputs[i, :] == outputs[j,:]))
def group_cover(group):
x = set()
for g in group:
x.update(g)
return len(x)
def group_closed(group, transitions):
for g in group:
for j in range(transitions.shape[1]):
implied = set()
for i in g:
if transitions[i, j] != -1:
implied.add(transitions[i, j])
flag = False
for next_g in group:
if implied.issubset(next_g):
flag = True
if not flag:
return False
return True
def minimize_table(transitions, outputs, initial_state_old):
pairs = dict()
for i in range(outputs.shape[0]):
for j in range(i + 1, outputs.shape[0]):
if is_pair_aligned(i, j, outputs):
l = set()
for a in range(outputs.shape[1]):
next_i, next_j = transitions[i, a], transitions[j, a]
next_i, next_j = min(next_i, next_j), max(next_i, next_j)
if next_i != -1 and next_j != -1 and (next_i, next_j) != (i, j) and next_i != next_j:
l.add((next_i, next_j))
if len(l) == 0:
pairs[(i, j)] = True
else:
pairs[(i, j)] = l
else:
pairs[(i, j)] = False
changed = True
while changed:
changed = False
for k in pairs:
if type(pairs[k]) == set:
for p in pairs[k]:
if not pairs[p]:
pairs[k] = False
changed = True
for i in range(outputs.shape[0]):
for j in range(i + 1, outputs.shape[0]):
if type(pairs[(i, j)]) == set:
pairs[(i, j)] = True
candidates = [set([x for x in range(1, outputs.shape[0])]),
set([0] + [x for x in range(1, outputs.shape[0]) if pairs[(0, x)]])]
#print(str(0 + 1) + ")", [[x + 1 for x in cand] for cand in candidates])
#print(str(0 + 1) + ")", [[x for x in cand] for cand in candidates])
for i in range(1, outputs.shape[0] - 1):
new_candidates = []
for cand in candidates:
if i in cand:
a = cand.copy()
a.remove(i)
b = {x for x in cand if pairs.get((i, x), True)}
if b == cand:
new_candidates.append(cand)
else:
new_candidates.append(a)
new_candidates.append(b)
else:
new_candidates.append(cand)
without_sub_groups = []
for cand in new_candidates:
flag = True
for cand2 in new_candidates:
if cand.issubset(cand2) and len(cand) != len(cand2):
flag = False
break
if flag and cand not in without_sub_groups:
without_sub_groups.append(cand)
candidates = without_sub_groups
#print(str(i + 1) + ")", [[x for x in cand] for cand in candidates])
#print(str(i + 1) + ")", [[x + 1 for x in cand] for cand in candidates])
num_of_groups = 1
while num_of_groups <= len(candidates):
for group in combinations(candidates, num_of_groups):
if group_cover(group) == outputs.shape[0] and group_closed(group, transitions):
final_transitions = np.zeros((len(group), outputs.shape[1]), dtype=int)
final_outputs = np.zeros((len(group), outputs.shape[1]), dtype=int)
for i, g in enumerate(group):
for j in range(outputs.shape[1]):
t = 0 # default value
next_group = set()
o = 1 # default value
for item in g:
if transitions[item, j] != -1:
next_group.add(transitions[item, j])
if outputs[item, j] != 2:
o = outputs[item, j]
if len(next_group) > 0:
t = [idx for idx, next in enumerate(group) if next_group.issubset(next)][0]
final_transitions[i, j] = t
final_outputs[i, j] = o
initial_state_new = [idx for idx, g in enumerate(group) if {initial_state_old}.issubset(g)][0]
return final_transitions, final_outputs, initial_state_new
num_of_groups += 1
def mealy_from_table(transitions, outputs, init_state_idx, alphabet):
states = []
states_dict = {}
for i in range(transitions.shape[0]):
states.append(MealyState(str(i)))
states_dict[str(i)] = states[-1]
for i in range(transitions.shape[0]):
for j in range(transitions.shape[1]):
states[i].transitions[alphabet[j]] = states_dict[str(transitions[i, j])]
states[i].output_fun[alphabet[j]] = str(outputs[i,j])
return MealyMachine(states[init_state_idx], states)
def dfa_from_table(transitions, outputs, init_state_idx, alphabet):
states = []
states_dict = {}
counter = 0
for i in range(transitions.shape[0]):
for j in range(transitions.shape[1]):
k = (transitions[i, j], outputs[i, j])
if k not in states_dict:
states.append(DfaState(str(counter)))
states_dict[k] = states[-1]
counter += 1
if (init_state_idx, 0) not in states_dict: # initial state should be accepted (not a bug)
states.append(DfaState(counter))
states_dict[(init_state_idx, 0)] = states[-1]
counter += 1
for k, s in states_dict.items():
for j in range(transitions.shape[1]):
s.transitions[alphabet[j]] = states_dict[(transitions[k[0], j], outputs[k[0], j])]
s.is_accepting = bool(k[1])
return Dfa(states_dict[(init_state_idx, 0)], states)
def find_minimal_consistent_dfa(dfa3: Automaton):
from aalpy.utils import save_automaton_to_file
transitions, outputs, init_state_idx = dfa3_to_tables(dfa3)
final_transitions, final_outputs, init_state_idx = minimize_table(transitions, outputs, init_state_idx)
return dfa_from_table(final_transitions, final_outputs, init_state_idx, dfa3.get_input_alphabet()), mealy_from_table(final_transitions, final_outputs, init_state_idx, dfa3.get_input_alphabet())