SageMath is a free open-source mathematics software system. Together with C. Heuberger and D. Krenn, we extended SageMath to include finite state machines, in particular automata and transducers.
The first version of SageMath including our contribution was 5.13. The documentation of the module can be found at the Sage Reference Manual. There we also included lots of examples.
Another possibility is to read our tutorial Automata in
SageMath—Combinatorics meets Theoretical Computer Science, where we introduce automata and explain how you can use them in SageMath.
A general introduction to SageMath can be found at Sage Reference Manual. Or you take a look at my presentation (using parts of presentations by William Stein, University of Washington, Clemens Heuberger, Alpen-Adria-Universität Klagenfurt).