# Büchi Store: an open repository of \(\omega \)-automata

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## Abstract

We introduce Büchi Store, an open repository of Büchi automata and other types of \(\omega \)-automata for model-checking practice, research, and education. The repository contains Büchi automata and their complements for common specification patterns and numerous temporal formulae. These automata are made as small as possible by various construction techniques in view of the fact that smaller automata are easier to understand and often help in speeding up the model-checking process. The repository is open, allowing the user to add automata that define new languages or are smaller than existing equivalent ones. Such a collection of Büchi automata is also useful as a benchmark for evaluating translation or complementation algorithms and as examples for studying Büchi automata and temporal logic. These apply analogously for other types of \(\omega \)-automata, including deterministic Büchi and deterministic parity automata, which are also collected in the repository. In particular, the use of smaller deterministic parity automata as an intermediary helps reduce the complexity of automatic synthesis of reactive systems from temporal specifications.

## Keywords

Linear Temporal Logic Temporal Formula Deterministic Automaton Translation Algorithm Recurrence Class## Notes

### Acknowledgments

This work was supported in part by National Science Council, Taiwan, under the grant NSC97-2221-E-002-074-My3. We thank Moshe Vardi and Wolfgang Thomas for teaching us so much about \(\omega \)-automata. Moshe’s enthusiasm in pursuing the automata-theoretic approach to model checking was a great source of inspiration for us to create Büchi Store. The diagram depicting the Temporal Hierarchy was learned from Wolfgang while he explained to us the use of DBW and DCW in the classification. Moshe’s Ph.D. student Seth Fogarty, during his visit to our group in the summer of 2009, witnessed the initiation of Büchi Store and made several useful comments. We thank Barbara Jobstmann whose suggestion of including deterministic parity automata prompted us to expand the Store to its current scope. The idea of maintaining a containment partial order of the language-equivalence classes should be shared with a participant of ETAPS 2011 whose name we could not recall; we thank him as well. Finally, we thank the three anonymous reviewers whose constructive and very detailed comments have helped improve the paper tremendously.

## Supplementary material

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