Advanced Ramsey-Based Büchi Automata Inclusion Testing

  • Parosh Aziz Abdulla
  • Yu-Fang Chen
  • Lorenzo Clemente
  • Lukáš Holík
  • Chih-Duo Hong
  • Richard Mayr
  • Tomáš Vojnar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6901)


Checking language inclusion between two nondeterministic Büchi automata \(\mathcal A\) and \(\mathcal B\) is computationally hard (PSPACE-complete). However, several approaches which are efficient in many practical cases have been proposed. We build on one of these, which is known as the Ramsey-based approach. It has recently been shown that the basic Ramsey-based approach can be drastically optimized by using powerful subsumption techniques, which allow one to prune the search-space when looking for counterexamples to inclusion. While previous works only used subsumption based on set inclusion or forward simulation on \(\mathcal A\) and \(\mathcal B\), we propose the following new techniques: (1) A larger subsumption relation based on a combination of backward and forward simulations on \(\mathcal A\) and \(\mathcal B\). (2) A method to additionally use forward simulation between \(\mathcal A\) and \(\mathcal B\). (3) Abstraction techniques that can speed up the computation and lead to early detection of counterexamples. The new algorithm was implemented and tested on automata derived from real-world model checking benchmarks, and on the Tabakov-Vardi random model, thus showing the usefulness of the proposed techniques.


Forward Simulation Subsumption Relation States Trans Proper Pair Language Inclusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Parosh Aziz Abdulla
    • 1
  • Yu-Fang Chen
    • 2
  • Lorenzo Clemente
    • 3
  • Lukáš Holík
    • 1
    • 4
  • Chih-Duo Hong
    • 2
  • Richard Mayr
    • 3
  • Tomáš Vojnar
    • 4
  1. 1.Uppsala UniversitySweden
  2. 2.Academia SinicaTaiwan
  3. 3.University of EdinburghUK
  4. 4.Brno University of TechnologyCzech Republic

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