Implement NFA algorithm (based on Python)

Posted by Unknown User on Tue, 12 Oct 2021 07:04:29 +0200

reference resources: Python implements DFA deterministic finite automata and NFA non deterministic finite automata_ Blog of remanufacturing P - CSDN blog

Ideas for solving problems

Design of data structure

Referring to the definition of NFA, NFA is a 5-tuple: M = (Q, ∑, Δ, s, F)

Where: Q is the finite set of states

   Σ is a finite alphabet

   s is the start state

   F contained in Q, end state set

  Δ Set of state transition functions

Solution algorithm:

NFA identification string: there are many possible paths for a string to pass through the NFA. As long as there is one that can finally reach the end state, the NFA can identify the string. Therefore, just get the set of states that the string finally reaches through the NFA and check whether there is an end state. If it exists, NFA can recognize this string, otherwise it cannot.

We should also consider the problem of empty character e, the set of states that a state can reach through empty character e, that is, the problem of empty closure of a state needs to be considered. If I is a subset of a set of States, I will have an empty closure set, which is recorded as ε- closure(I). The empty closure set is also a state set, and its elements conform to the following points: all elements of I are elements of the empty closure set; For each element in I, start from that element and pass through any bar ε The states that an arc can reach are elements of an empty closure set.

In class NFA, four functions are designed, which are read_string(),e_closure(),next_state(),match_final_state().

Function read_string(input_str): read the input string and judge whether it can be accepted by NFA

Function e_closure(state): find the empty closure of a state (the idea of BFS)

Function next_state(current_states, c): the next state set reached by the current state set through the character C

Function match_final_state(final_current_states): the final state matches the accepted state

"""Design to recognize strings NFA"""
import string
from collections import deque

class NFA:
    def __init__(self, states, symbols, t_state, start_state, final_state):     # initialization
        self.states = states                    # State set
        self.symbols = symbols                  # Input symbol set / alphabet
        self.t_state = t_state                  # State transition function
        self.start_state = start_state          # Start state
        self.final_state = final_state          # End state

    def read_string(self, input_str):           # Read string to enter NFA authentication
        for c in input_str:                     # Judge whether the string meets the alphabet
            if c not in self.symbols:
                print('Illegal character in string')

        next_states = [self.start_state]
        for i in str:
            next_states = self.next_state(next_states, i)

        result = self.match_final_state(next_states)
        if result == True:
            print('NFA This string is acceptable')
            print('NFA The string cannot be received')

    def e_closure(self, state):                 # Find the empty closure of a state
        d_state = deque()                       # Dual ended queue, storing intermediate status
        empty_bag = []                          # Empty closure of a state
        while (len(d_state)):
            current_state = d_state[0]
            if current_state in self.t_state.keys():  # If the current state exists
                if 'e' in self.t_state[current_state].keys():  # If there is a null character transfer
                    for s in self.t_state[current_state]['e']:
                        if s not in empty_bag:  # If the state is not in an empty closure
                            d_state.append(s)   # Queue and join the state arrived via e into the empty closure
            d_state.popleft()                   # Throw the current state
        return empty_bag

    def next_state(self, current_states, c):    # The collection of the next state that the current state can reach through a character, including empty closures
        next_states = []                        # The next state set, including the set of empty closures of the next state set
        for state in current_states:
            if state in self.t_state.keys():
                if c in self.t_state[state].keys():
                    n_states = self.t_state[state][c]
                    for s in n_states:          # Gets the empty closure of the next state set
                        s_closure = self.e_closure(s)
                        for s_c in s_closure:   # Add the set of empty closures to the next state set
                            if s_c not in next_states:
        print('State transition:')
        print(current_states, end=' ')
        print('-' + c + '->', end=' ')
        return next_states                      # Returns the set of the next state obtained / the state set through the character c

    def match_final_state(self, final_current_states: list) ->bool :         # The final state matches the end state
        for state in final_current_states:
            if state in self.final_state:
                return True
        return False

if __name__ == '__main__':
    states = ['q1', 'q2', 'q3', 'q4']   # NFA state set
    symbols = ['0', '1']                # NFA alphabet
    t_state = {
        'q1': {
            '0': ['q1'],
            '1': ['q1', 'q2']
        'q2': {
            'e': ['q3'],
            '0': ['q3']
        'q3': {
            '1': ['q4']
        'q4': {
            '0': ['q4'],
            '1': ['q4']
    }                     # State transition function
    start_state = 'q1'                  # Start state
    final_state = ['q4']                # End state set

    while True:
        str = input("Please enter the test string:")
        if str == 'exit':
        nfa = NFA(states, symbols, t_state, start_state, final_state)

Topics: Python Algorithm data structure