Convert finite state machine to regular expression

Question

Is there a tool (or an algorithm) to convert a finite state machine into a regular expression?

(not the other way around, that would be easy).

Answer 1

I believe the best tool I have used is greenery. It is a FSM/regex conversion library for python. You can read more about the library here and the algorithm used is well described here.

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Example

The model that can be found on the website can be converted like this:

from greenery import fsm, lego

A, B, C, D, E = range(5)
a, b = 'a', 'b'

# create the FSM
machine = fsm.fsm(
    alphabet = {a, b},
    states   = {A, B, C, D, E},
    initial  = A,
    finals   = {C, E},
    map      = {
            A : {a: B, b: D},
            B : {a: C, b: E},
            C : {a: C, b: E},
            D : {a: B, b: D},
            E : {a: B, b: D}
    },
)

# convert it to regex
rex = lego.from_fsm(machine)

The output is the following:

>>> print(machine)

  name final? a b
------------------
* 0    False  1 3
  1    False  2 4
  2    True   2 4
  3    False  1 3
  4    True   1 3

>>> print(rex)

b*a((a*(a|b+))?ba)*(a+b?|b)

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Note

The version on PYPI has some problem with assertions, and the github version has some problems with the memory, but the combination python 3.x + github version is awesome.