Conversion from DFA to NFA does not properly handle state names of mixed data types

I found the following bug: nfa._add_new_state introduces integers into the set of states.

Current code is:

    def _add_new_state(state_set, start=0):
        """Adds new state to the state set and returns it"""
        new_state = start
        while new_state in state_set:
            new_state += 1

        state_set.add(new_state)

        return new_state

which could be fixed, for example, in this way:

    def _add_new_state(state_set, start=0):
        """Adds new state to the state set and returns it"""
        new_state = start
        while str(new_state) in state_set:
            new_state += 1

        state_set.add(str(new_state))

        return str(new_state)

EDIT: this bugfix actually runs into other problems later - this is just an idea

---

This can lead to logic problems later. For example the following code fails:

from automata.fa.dfa import DFA
from automata.fa.nfa import NFA

A = NFA(
    states={'0', '1'},
    input_symbols={'0'},
    transitions={'0': {'0': {'1'}}, '1': {'0': {'1'}}},
    initial_state='0',
    final_states={'1'}
)

print(A.reverse().states)

B = DFA.from_nfa(A.reverse())

assert(A.accepts_input('00')==B.accepts_input('00'))

[eliotwrobson]

@caleb531 It looks like the test you wrote checks for the fact that the _add_new_state now has better support for integer string state names, but there are still issues when manually constructing an NFA.

The following (somewhat contrived) assertion fails:

A = NFA(
    states={1, '1'},
    input_symbols={'0'},
    transitions={1: {'0': {'1'}}, '1': {'0': {'1'}}},
    initial_state=1,
    final_states={'1'}
)

B = DFA.from_nfa(A)

assert A.accepts_input('00') == B.accepts_input('00')

[caleb531]

@colette-b Good news! I was actually able to refactor _add_new_state to correctly handle non-string states, thus fixing your original example. All other automated tests are passing too, so there should be no regressions from this refactor.

In case you’re curious, here is the new implementation:

@staticmethod
def _add_new_state(state_set, start=0):
    """Adds new state to the state set and returns it"""
    new_state = start
    # coercing the state names to strings is the key!
    str_state_set = {str(state) for state in state_set}
    while str(new_state) in str_state_set:
        new_state += 1

    state_set.add(new_state)

    return new_state