# Generic Emptiness Check for Fun and Profit

### From LRDE

- Authors
- Christel Baier, František Blahoudek, Alexandre Duret-Lutz, Joachim Klein, David Müller, Jan Strejček
- Where
- Proceedings of the 17th International Symposium on Automated Technology for Verification and Analysis (ATVA'19)
- Type
- inproceedings
- Publisher
- Springer
- Keywords
- Spot
- Date
- 2019-07-29

## Abstract

We present a new algorithm for checking the emptiness of **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega}**
-automata with an Emerson-Lei acceptance condition (i.e., a positive Boolean formula over sets of states or transitions that must be visited infinitely or finitely often). The algorithm can also solve the model checking problem of probabilistic positiveness of MDP under a property given as a deterministic Emerson-Lei automaton. Although both these problems are known to be NP-complete and our algorithm is exponential in general, it runs in polynomial time for simpler acceptance conditions like generalized Rabin, Streett, or parity. In fact, the algorithm provides a unifying view on emptiness checks for these simpler automata classes. We have implemented the algorithm in Spot and PRISM and our experiments show improved performance over previous solutions.

## Documents

## Bibtex (lrde.bib)

@InProceedings{ baier.19.atva, author = {Christel Baier and Franti\v{s}ek Blahoudek and Alexandre Duret-Lutz and Joachim Klein and David M\"uller and Jan Strej\v{c}ek}, title = {Generic Emptiness Check for Fun and Profit}, booktitle = {Proceedings of the 17th International Symposium on Automated Technology for Verification and Analysis (ATVA'19)}, year = {2019}, volume = {?????}, series = {Lecture Notes in Computer Science}, pages = {???--???}, month = oct, publisher = {Springer}, note = {To appear}, abstract = {We present a new algorithm for checking the emptiness of $\omega$-automata with an Emerson-Lei acceptance condition (i.e., a positive Boolean formula over sets of states or transitions that must be visited infinitely or finitely often). The algorithm can also solve the model checking problem of probabilistic positiveness of MDP under a property given as a deterministic Emerson-Lei automaton. Although both these problems are known to be NP-complete and our algorithm is exponential in general, it runs in polynomial time for simpler acceptance conditions like generalized Rabin, Streett, or parity. In fact, the algorithm provides a unifying view on emptiness checks for these simpler automata classes. We have implemented the algorithm in Spot and PRISM and our experiments show improved performance over previous solutions.} }