Commit ed41bb02 authored by Kateřina Sloupová's avatar Kateřina Sloupová
Browse files

DFA equivalence and emptiness; NFA can epsilon

parent e7408f3b

demo.py

+40 −13
Original line number Diff line number Diff line 
from parser import Parser

from reg_automata import Character, State, DFA, NFA

from reg_automata import Character, State, DFA, NFA, NFAE, Eps

from reg_automata import Composition as comp

from reg_grammars import REG, Terminal, Nonterminal

from typing import Set, Dict, Tuple, Union

from copy import deepcopy





def make_dfa(states: Set[str], characters: Set[str],
@@ -66,6 +67,23 @@ def nfa_1(): 
    nfa = NFA({q0, q1, q2}, {a}, transition, q0, {q1, q2})

    return nfa



def nfa_e():

    q0 = State("q0")

    q1 = State("q1")

    q2 = State("q2")

    q3 = State("q3")

    q4 = State("q4")

    a = Character("a")

    b = Character("b")

    c = Character("c")

    d = Character("d")

    e = Eps()

    transition: Dict[Tuple[State, Union[Character, Eps]], Set[State]] = \

                {(q0, e): {q1}, (q1, a): {q0}, (q1, d): {q3}, (q1, e): {q2},

                 (q2, a): {q3}, (q3, e): {q4}, (q4, b): {q3}, (q4, c): {q2}}

    nfae = NFAE({q0, q1, q2, q3, q4}, {a, b, c, d}, transition, q0, {q2})

    return nfae



def main():

    dfa_1 = make_dfa({"q_0", "q_1"}, {"a"}, {("q_0", "a"): "q_1", ("q_1", "a"): "q_1"}, "q_0", {"q_1"})

    dfa_2 = make_dfa({"r_0", "r_1", "r_2"}, {"a", "b"}, {("r_0", "a"): "r_1", ("r_0", "b"): "r_1",
@@ -138,17 +156,18 @@ def main(): 
    print("DFA.eliminate_unreachable()")

    print("Add new state (also to transition) and eliminate unreachable states.")



    dfa_x = deepcopy(dfa_1)

    q_x = State("q_x")

    a = Terminal("a")

    dfa_1.states.add(q_x)

    dfa_1.final.add(q_x)

    dfa_1.transition[q_x, a] = q_x

    dfa_x.states.add(q_x)

    dfa_x.final.add(q_x)

    dfa_x.transition[q_x, a] = q_x

    print()

    print("DFA with new state:")

    print(parser.dfa_to_str(dfa_1, True))

    print(parser.dfa_to_str(dfa_x, True))

    print()

    print("DFA without unreachable states:")

    eliminated = dfa_1.eliminate_unreachable()

    eliminated = dfa_x.eliminate_unreachable()

    print(parser.dfa_to_str(eliminated, True))

    print()
@@ -158,7 +177,6 @@ def main(): 
    print()

    print(parser.dfa_to_str(dfa_3, True))





    print()

    print("Minimal DFA:")

    minimal = dfa_3.minimize()
@@ -191,6 +209,15 @@ def main(): 
    print(parser.nfa_to_str(regdfa, True))

    print()



    print("__________________________________")

    print("DFA.is_empty(), DFA.is_equivalent()")

    print("Emptiness with counterexample and equivalence \n"

          "of DFA through intersections with complements.")

    print()

    print("is dfa3 empty?", dfa_3.is_empty())

    print("dfa3 and canonical dfa3: ", dfa_3.is_equivalent(canonical), ", should be True")

    print()



    print("__________________________________")

    print("NFA.determinize()")

    print("Determinization of NFA to DFA:")
@@ -200,12 +227,12 @@ def main(): 
    print(parser.dfa_to_str(det, True))



    print("__________________________________")

    print("DFA.is_equivalent()")

    print("Equivalence of DFAs through intersections with complements.")

    print("NFAE.eliminate_epsilon()")

    print("Elimination of epsilon steps in NFA.")

    nfae = nfa_e()

    print(parser.nfa_to_str(nfae))

    print()



    print(dfa_3.is_equivalent(canonical), ", should be True")

    print()



    nfa_elim = nfae.eliminate_epsilon()

    print(parser.nfa_to_str(nfa_elim, True))



main()
 
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objects.py

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parser.py

+10 −5
Original line number Diff line number Diff line 
from typing import List, Dict, Tuple, Optional

from typing import List, Dict, Tuple, Optional, Union

import re

from reg_automata import DFA, NFA

from reg_automata import DFA, NFA, NFAE, Eps

from reg_grammars import REG, Terminal
@@ -89,7 +89,7 @@ class Parser: 
            return transition + "\n" + final





    def nfa_to_str(self, nfa: NFA, full : bool = False) -> str:

    def nfa_to_str(self, nfa: Union[NFA, NFAE], full : bool = False) -> str:



        # full - verbose description of DFA - only for development, dismiss later
@@ -108,7 +108,11 @@ class Parser: 
        transition = ""

        for key, set_states in nfa.transition.items():

            state_1, terminal = key

            transition += "(" + state_1.name + "," + terminal.name + ")={"

            if isinstance(terminal, Eps):

                char = "epsilon"

            else:

                char = terminal.name

            transition += "(" + state_1.name + "," + char + ")={"

            for state in set_states:

                transition += state.name + ","

            transition = transition[:-1] + "}\n"
@@ -128,7 +132,8 @@ class Parser: 
        else:

            return transition + "\n" + final



# TODO DFA/NFA to string are too similar

    def str_to_dfa(self, input: str):

        pass



# all: string <-> formal object

# reg

reg_automata.py

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reg_grammars.py

+2 −10

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