Here are some current tools for checking language inclusion of Buchi automata.

1. RABIT (Ramsey-based Buchi automata Inclusion Testing).

It implements a generalized version of the Ramsey-based method for Buchi automata inclusion checking with additional subsumption techniques using backward and forward simulation preorder. The latest version of the tool additionally uses generalized automata minimization techniques using good approximations of multipebble simulations and trace inclusions (see the LMCS 2019 on the RABIT tool page). Most recent version of the RABIT tool.

- GOAL tool. There are many other methods for checking Buchi automata inclusion/equivalence, e.g., Safra-based constructions, Muller-Schupp constructions, Safra-Pieteman construction, and Slice-based constructions. The GOAL tool implements many of these. On most instances RABIT performs better than GOAL and thus it can solve much larger instances.

• Richard Mayr, Lorenzo Clemente. Efficient reduction of nondeterministic automata with application to language inclusion testing. Logical Methods in Computer Science 15(1). 2019.
• Richard Mayr, Lorenzo Clemente. Advanced Automata Minimization. POPL 2013. Extended Technical Report EDI-INF-RR-1414.
• Richard Mayr, Parosh Aziz Abdulla, Yu-Fang Chen, Lorenzo Clemente, Lukás Holik, Chih-Duo Hong and Tomas Vojnar. Advanced Ramsey-based Buchi Automata Inclusion Testing. CONCUR 2011, volume 6901 in LNCS. 2011.
• Parosh Aziz Abdulla, Yu-Fang Chen, Lorenzo Clemente, Lukás Holík, Chih-Duo Hong, Richard Mayr, Tomás Vojnar: Simulation Subsumption in Ramsey-Based Büchi Automata Universality and Inclusion Testing. CAV 2010: 132-147