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nfa2dfa-toefl.py
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nfa2dfa-toefl.py
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#!/usr/bin/python
import sys
from copy import deepcopy
from itertools import combinations
def read_rules(line): # read in the rules and update nfa_machine
global nfa_machine
rules = nfa_machine["transfer_function"]
line_list = line.split(',')
init_state = line_list[0]
input_symbol = line_list[1]
new_state = line_list[2]
if (input_symbol not in rules[init_state]):
rules[init_state][input_symbol]= []
rules[init_state][input_symbol].append(new_state)
def get_reachable_states(state): #for a state, recursively call this function to find all the states it can reach with ~
detected_states.append(state)
if('~' in nfa_machine["transfer_function"][state]):
raw_states = nfa_machine["transfer_function"][state]['~']
to_add = list(set(raw_states).difference(set(reachable_states)))
reachable_states.extend(to_add)
to_detect = list(set(raw_states).difference(set(detected_states)))
print("To detect: " + str(to_detect))
if(len(to_detect) > 0):
update_reachable_states(to_detect)
def update_reachable_states(state_list): # get reachable states for a list of states, in this function, we use for loop and call update_reachable_states
global reachable_states,detected_states
for state in state_list:
get_reachable_states(state)
def explore_individual (a_state, a_symbol): #for a state and a symbol, return a list of states that can be reached, do not consider ~
global nfa_machine
if(a_symbol in nfa_machine["transfer_function"][a_state]):
return nfa_machine["transfer_function"][a_state][a_symbol]
else:
return ''
def explore(states_to_explore):
#find the rule for a new state in dfa, and if the result state is new, we add it to list new_states and to_explore
global new_states,to_explore,state_map,nfa_machine, new_dfa_machine, reachable_states, detected_states
state_str = ''.join(states_to_explore)
if (state_str not in new_states):
new_states.append(state_str)
to_explore.append(state_str)
state_map[state_str] = states_to_explore
result = {}
for a_symbol in nfa_machine["alphabet"]:
result[a_symbol] = ""
temp_states = []
for a_state in states_to_explore:
a_result = explore_individual (a_state, a_symbol)
print ("For "+ str(a_state) + " and input " + str(a_symbol) +" we get " + str(a_result))
if (a_result != '' and (a_result not in temp_states)):
temp_states.append(a_result) #a_result can be a list
raw_list = []
if (len(temp_states) == 0):
result[a_symbol] = 'phi'
else:
for result_states in temp_states:
raw_list.extend(result_states)
raw_list = list(set(raw_list))
reachable_states = deepcopy(raw_list)
detected_states = []
update_reachable_states(reachable_states)
temp_list = deepcopy(reachable_states) #need to count in all the reach states for the result
temp_list.sort()
result[a_symbol] = ''.join(temp_list)
print(temp_list)
if (state_str not in new_dfa_machine["transfer_function"]): # add it to the rule
new_dfa_machine["transfer_function"][state_str] = {}
new_dfa_machine["transfer_function"][state_str][a_symbol] = result[a_symbol]
if (result[a_symbol] not in new_states):
new_states.append(result[a_symbol])
to_explore.append(result[a_symbol])
state_map[result[a_symbol]] = temp_list
print("We have a new state when explore: " + str(temp_list))
def gen_new_states(): # get the states for the new dfa machine, it's the power set of the original states
global nfa_machine, new_dfa_machine
new_dfa_machine["states"].append("phi")
original_states = nfa_machine["states"]
for i in range(1,len(original_states)+1):
tuple_list = list(combinations(original_states,i))
for t in tuple_list:
t = list(t)
t.sort()
new_state = ''.join(t)
new_dfa_machine["states"].append(new_state)
def check_accepting_states(states): # check if a set of states contain the accepting states in the original states, if yes, add it to the dfa states
global nfa_machine, new_dfa_machine
ac = ''.join(states)
for s in states:
if (s in nfa_machine["accepting_states"] and (ac not in new_dfa_machine["accepting_states"])):
new_dfa_machine["accepting_states"].append(ac)
break
def add_trap_rule(): # add the rule for the "phi" state
global nfa_machine, new_dfa_machine
new_dfa_machine["transfer_function"]['phi'] = {}
for symbol in nfa_machine["alphabet"] :
new_dfa_machine["transfer_function"]['phi'][symbol] = 'phi'
nfa_machine = {
"machine_name" : "",
"alphabet" : [],
"states" : [],
"start_state" : "",
"accepting_states" : [],
"rejected_states" : [],
"current_state" : "",
"transfer_function" : {}
}
new_dfa_machine = {
"machine_name" : "",
"alphabet" : [],
"states" : [], # by definition is the power set
"start_state" : "",
"accepting_states" : [],
"transfer_function" : {}
}
state_map = {}
reachable_states = []
detected_states = []
fa_file = sys.argv[1]
fa = open(fa_file, "r")
try: #read from the nfa definition and construct the machine, print the information at the same time
for i, line in enumerate(fa):
line = line.rstrip()
if i == 0:
if ":" in line:
colon = line.index(':')
machine_name = line[:colon]
nfa_machine["machine_name"] = machine_name
print ("Machine name: " + machine_name)
else:
machine_name = line
nfa_machine["machine_name"] = machine_name
print ("Machine name: " + machine_name)
elif i == 1:
alphabet = line.split(',')
nfa_machine["alphabet"] = alphabet
print("Alphabet: " + str(alphabet))
elif i ==2:
states = line.split(',')
nfa_machine["states"] = states
for state in states:
nfa_machine["transfer_function"][state] = {}
state_map[state] = [state]
print("States: " + str(states))
elif i == 3:
start_state = line
nfa_machine["start_state"] = start_state
print("Start state : " + start_state)
elif i ==4:
accepting_states = line.split(',')
rejected_states = list(set(states).difference(set(accepting_states)))
nfa_machine["accepting_states"] = accepting_states
nfa_machine["rejected_states"] = rejected_states
print("Accepting states : " + str(accepting_states))
else:
print("Rule "+ str(i-4) +" : "+ line)
read_rules(line)
except:
print "Cannot read the file"
finally:
fa.close()
to_explore = deepcopy(nfa_machine["states"])
new_states = deepcopy(to_explore)
new_states.append('phi')
new_dfa_machine["machine_name"] = nfa_machine["machine_name"] + " to DFA"
new_dfa_machine["alphabet"] = nfa_machine["alphabet"]
gen_new_states()
add_trap_rule()
while (len(to_explore)>0): # explore until nothing left
element_to_explore = to_explore[0]
print("The remain to explore is " + str(to_explore))
to_explore.pop(0)
reachable_states = deepcopy(state_map[element_to_explore])
detected_states = []
update_reachable_states(state_map[element_to_explore])
reachable_states.sort()
print("Reachable is " + str(reachable_states))
if(len(new_dfa_machine["start_state"])==0):
new_dfa_machine["start_state"] = ''.join(reachable_states)
check_accepting_states(reachable_states)
explore(reachable_states)
print(new_dfa_machine)
output_file_name = sys.argv[1].replace('.txt', '')+ "-DFA" +".csv"
output_file = open(output_file_name, "w")
try: #read from the nfa definition and construct the machine, print the information at the same time
output_file.write(new_dfa_machine["machine_name"] + "\n")
output_file.write(",".join(new_dfa_machine["alphabet"])+ "\n")
output_file.write(",".join(new_dfa_machine["states"])+ "\n")
output_file.write(new_dfa_machine["start_state"]+ "\n")
output_file.write(",".join(new_dfa_machine["accepting_states"])+ "\n")
for key1 in new_dfa_machine["transfer_function"]:
for key2 in new_dfa_machine["transfer_function"][key1]:
output_file.write(key1 + "," + key2+ "," + new_dfa_machine["transfer_function"][key1][key2]+ "\n")
except:
print "Cannot write to file"
finally:
output_file.close()