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FSM.py
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FSM.py
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from queue import SimpleQueue
from tabulate import tabulate
class FSM:
def __init__(self, sts=None, sgm=None):
"""
sts: tuples of states. sgm: tuples of alphabet, '^' will be considered as
epsilon.
"""
self.states = dict()
if sts is not None:
for s in sts:
self.states[s] = State(s)
if sgm is not None:
self.sigma = sgm
else:
self.sigma = tuple("ab")
self.initial_state = None # name of state
self.accepting_states = set() # names of state
def add_state(self, name):
self.states[name] = State(name)
def set_initial(self, state):
self.initial_state = state
def add_accepting(self, state):
self.accepting_states.add(state)
self.states[state].accepting = True
# add transition (next state) from s1 to s2
def add_transition(self, s1, label, s2):
if label in self.states[s1].next:
self.states[s1].next[label].append(s2)
else:
self.states[s1].next[label] = [s2]
def eps(self, state_name):
state = self.states[state_name]
result = {state}
process = SimpleQueue()
process.put(state)
while not process.empty():
p = process.get()
if "^" in p.next:
nexts = p.next["^"]
for n in nexts:
next_state = self.states[n]
if next_state not in result:
result.add(next_state)
process.put(next_state)
return result
def ndfsm_simulate(self, w):
print("\nNDSFM Simulate")
st = self.eps(self.initial_state)
st1 = set()
for c in w:
st1 = set()
for q in st:
if c in q.next:
p = q.next[c]
for p_state in p:
st1 |= self.eps(p_state)
st = st1
if st == set():
break
acc_set = {self.states[x] for x in self.accepting_states}
return (st & acc_set) != set()
def dfsm_simulate(self, w):
print("\nDFSM Simulate")
st = self.states[self.initial_state]
for c in w:
st = self.states[st.next[c][0]]
acc_set = {self.states[x] for x in self.accepting_states}
return st in acc_set
def ndfsm_to_dfsm(self):
"""Returns quintuple (K, Σ, δ, s, A) of tuples K, Σ, δ, A and string s.
K -> states.
Σ -> alphabet.
δ -> transition function.
s -> starting state.
A -> accepting states."""
print("\nNDFSM to DFSM")
epsilons = dict()
for s in self.states:
epsilons[s] = self.eps(s)
start = epsilons[self.initial_state]
active_state = set()
deltas = set()
process = SimpleQueue()
start_tuple = self.state_set_to_tuple(start)
# active_state.add(start_tuple)
process.put(start_tuple)
data = [] # to print tabulate
while not process.empty():
data_row = [] # to print tabulate
state_tuple = process.get()
if state_tuple not in active_state:
active_state.add(state_tuple)
data_row.append(self.state_tuple_to_string(state_tuple))
for c in self.sigma:
new_state = set()
for q in state_tuple:
if c in q.next:
p = q.next[c]
for p_state in p:
new_state |= self.eps(p_state)
new_state_tuple = self.state_set_to_tuple(new_state)
deltas.add((state_tuple, c, new_state_tuple))
data_row.append(self.state_tuple_to_string(new_state_tuple))
if new_state_tuple not in active_state:
# active_state.add(new_state_tuple)
process.put(new_state_tuple)
else:
continue
data.append(data_row)
active_state_name = {tuple(x.name for x in y) for y in active_state}
new_acc_states = {
x for x in active_state_name if (set(x) & self.accepting_states != set())
}
new_init_state = self.state_tuple_to_string(start_tuple)
print(tabulate(data, headers=["Active State"] + list(self.sigma)))
print("accepting states:", new_acc_states)
print("initial state:", new_init_state)
# print(data)
return (
tuple(active_state_name),
self.sigma,
tuple(deltas),
new_init_state,
tuple(new_acc_states),
)
def state_set_to_tuple(self, states):
states = list(states)
states.sort(key=lambda x: x.name)
states = tuple(states)
return states
def state_tuple_to_string(self, states):
if len(states) == 0:
return "{}"
return ",".join(str(s.name) for s in states)
def min_dfsm(self):
print("\nMinimize DFSM")
acc = list(sorted(list(self.accepting_states)))
k_min_acc = list(sorted(list(self.states.keys() - self.accepting_states)))
classes = [acc, k_min_acc]
step = 1
while True:
print("Step", step)
print("classes:", classes)
step += 1
new_classes = []
to_tabulate = []
for e in classes:
outputs = []
for q in e:
e_output = []
for c in self.sigma:
e_output.append(((q, c), self.get_next_class(q, c, classes)))
outputs.append(e_output)
tmp_to_tabulate = [q]
for i in range(len(self.sigma)):
tmp_to_tabulate.append(e_output[i][1])
to_tabulate.append(tmp_to_tabulate)
to_tabulate.append(["-"] * (len(self.sigma) + 1))
new_classes.extend(self.get_new_classes(outputs))
print(tabulate(to_tabulate, headers=["State"] + list(self.sigma)))
if classes == new_classes:
break
classes = new_classes
def get_next_class(self, s, c, classes):
state = self.states[s]
next_state = state.next[c][0]
for next_class in classes:
if next_state in next_class:
return next_class
raise Exception("No class found")
def get_new_classes(self, outputs):
new_classes = []
equivalence_class = []
for item in outputs:
item_output = []
for i in range(len(self.sigma)):
item_output.append(item[i][1])
if item_output in equivalence_class:
idx = equivalence_class.index(item_output)
new_classes[idx].append(item[0][0][0])
else:
equivalence_class.append(item_output)
new_classes.append([item[0][0][0]])
return new_classes
def ndfsm_to_regex(self):
"""Returns string of regular expression from rip states.
Please make sure the ndfsm fulfills the precondition.
Initial state should be named init and final state should be
named acc.
WARNING: HAVE NOT BEEN THOROUGHLY TESTED, USE WITH CAUTION
"""
print("\nNDFSM TO REGEX")
regex = ""
cur_states = list(self.states.keys())
to_tabulate = self.create_transition_table()
cols = cur_states.copy()
cols.remove("init")
header = ["State"] + cols
print(tabulate(to_tabulate, headers=header))
print("\n")
while len(to_tabulate) > 1:
encodings = dict(enumerate(cols[:-1], 1))
encodings = {str(k): str(v) for k, v in encodings.items()}
print("Rip state (", end="")
print(", ".join(":".join(_) for _ in encodings.items()), end="")
print("): ", end="")
to_rip = input()
state_to_rip = encodings[to_rip]
new_cols = cols.copy()
new_cols.remove(state_to_rip)
col_indexes = dict()
for i in range(1, len(header)):
col_indexes[header[i]] = i
ripped_row = []
for row in to_tabulate:
if row[0] == state_to_rip:
ripped_row = row
break
to_tabulate = [None] + to_tabulate # convert to one-based indexing
new_table = []
ripped_loop = ripped_row[col_indexes[state_to_rip]]
if ripped_loop != "∅":
if "U" in ripped_loop:
ripped_loop = "(" + ripped_loop + ")*"
else:
ripped_loop = ripped_loop + "*"
else:
ripped_loop = ""
for i in range(1, len(to_tabulate)):
label = to_tabulate[i][0]
if label == state_to_rip:
continue
cur_row = to_tabulate[i]
new_row = [label] + ["."] * (len(to_tabulate[i]) - 2)
idx = 0
for j in range(len(cols)):
if cols[j] == state_to_rip:
continue
idx += 1
this_to_dest = cur_row[col_indexes[cols[j]]]
this_to_ripped = cur_row[col_indexes[state_to_rip]]
ripped_to_dest = ripped_row[col_indexes[cols[j]]]
if this_to_dest != "∅":
if len(this_to_dest) > 1 and this_to_dest.count("U") > 1:
this_to_dest = "(" + this_to_dest + ")"
else:
this_to_dest = ""
if this_to_ripped == "∅" or ripped_to_dest == "∅":
new_row[idx] = this_to_dest if this_to_dest != "" else "∅"
continue
temp_regex = (
"(" + this_to_dest + ")U"
if this_to_dest != "" and "U" in this_to_dest
else this_to_dest + "U"
if this_to_dest != ""
else ""
)
if this_to_ripped == "^":
this_to_ripped = ""
else:
if len(this_to_ripped) > 1 and this_to_ripped.count("U"):
this_to_ripped = f"({this_to_ripped})"
if ripped_to_dest == "^":
ripped_to_dest = ""
else:
if len(ripped_to_dest) > 1 and ripped_to_dest.count("U"):
ripped_to_dest = f"({ripped_to_dest})"
this_to_ripped_to_dest = (
f"{this_to_ripped}{ripped_loop}{ripped_to_dest}"
)
if "U" in this_to_ripped_to_dest and temp_regex != "":
temp_regex += "(" + this_to_ripped_to_dest + ")"
else:
temp_regex += this_to_ripped_to_dest
new_row[idx] = temp_regex
pass
new_table.append(new_row)
to_tabulate = new_table
cols = new_cols
header = ["State"] + cols
print(tabulate(to_tabulate, headers=header))
print("\n")
def create_transition_table(self):
cur_states = list(self.states.keys())
table = []
cols = cur_states.copy()
cols.remove("init")
for s in cur_states:
if s == "acc":
continue
cur_row = []
cur_row.append(s)
st = self.states.get(s)
for next_s in cols:
ans = ""
for k, v in st.next.items():
if next_s in v:
ans += k + "U"
if ans == "":
ans = "∅"
else:
ans = ans[:-1]
cur_row.append(ans)
table.append(cur_row)
return table
class State:
def __init__(self, name):
self.name = name
self.next = dict()
self.accepting = False
def main():
# minimize dfsm demo
# visualization of a: https://prnt.sc/sRIxEdmVPSr9
a = FSM(sts=(1, 2, 3, 4, 5, 6), sgm=("a", "b"))
a.add_transition(1, "a", 2)
a.add_transition(1, "b", 4)
a.add_transition(2, "a", 3)
a.add_transition(2, "b", 6)
a.add_transition(3, "a", 2)
a.add_transition(3, "b", 4)
a.add_transition(4, "a", 6)
a.add_transition(4, "b", 5)
a.add_transition(5, "a", 2)
a.add_transition(5, "b", 4)
a.add_transition(6, "a", 6)
a.add_transition(6, "b", 6)
a.add_accepting(2)
a.add_accepting(4)
a.set_initial(1)
a.min_dfsm()
# convert ndfsm to dfsm demo
# visualization of b: https://prnt.sc/Zf3bA5kSKkvL
b = FSM(sts=(1, 2, 3, 4, 5, 6, 7, 8), sgm=("a", "b", "c"))
b.add_transition(1, "b", 1)
b.add_transition(1, "^", 2)
b.add_transition(2, "^", 7)
b.add_transition(2, "b", 3)
b.add_transition(2, "b", 5)
b.add_transition(3, "a", 4)
b.add_transition(3, "c", 4)
b.add_transition(4, "c", 2)
b.add_transition(4, "c", 7)
b.add_transition(5, "a", 6)
b.add_transition(5, "b", 6)
b.add_transition(6, "^", 2)
b.add_transition(6, "c", 2)
b.add_transition(6, "c", 7)
b.add_transition(7, "b", 8)
b.set_initial(1)
b.add_accepting(8)
b.ndfsm_to_dfsm()
# convert ndfsm to regex demo
# https://docs.google.com/spreadsheets/d/1Esfdl43IZ9DZb-F0cFK4ZkthGIqfWfHlqPPFqjTdG_E/edit#gid=0
# q5 -> acc
c = FSM(sts=("init", "A", "B", "C", "D", "acc"), sgm=("a", "b", "c"))
c.set_initial("init")
c.add_accepting("acc")
c.add_transition("init", "^", "A")
c.add_transition("A", "a", "B")
c.add_transition("A", "b", "A")
c.add_transition("A", "c", "A")
c.add_transition("A", "^", "acc")
c.add_transition("B", "a", "B")
c.add_transition("B", "b", "D")
c.add_transition("B", "c", "A")
c.add_transition("B", "^", "acc")
c.add_transition("C", "b", "A")
c.add_transition("C", "c", "A")
c.add_transition("C", "^", "acc")
c.add_transition("D", "a", "B")
c.add_transition("D", "b", "A")
c.add_transition("D", "c", "C")
c.add_transition("D", "^", "acc")
c.ndfsm_to_regex()
# input 3, 3, 2, 1 to rip state C, D, B, then A
def print_eps(e):
for i in e:
print(i.name, end=" ")
print()
if __name__ == "__main__":
main()