While the minimization problem for deterministic Büchi word automata is known to be NP-complete, several fundamental problems around it are still open. This includes the complexity of minimzation for transition-based automata, where acceptance is defined with respect to the set of transitions that a run traverses infinitely often, and minimization for good-for-games (GFG) automata, where nondeterminism is allowed, yet has to be resolved in a way that only depends on the past. Of special interest in formal verification are liveness properties, which state that something “good” eventually happens. Liveness languages constitute a strict fragment of ω -regular languages, which suggests that minimization of automata recognizing liveness languages may be easier, as is the case for languages recognizable by weak automata, in particular safety languages. We define three classes of liveness, and study the minimization problem for automata recognizing languages in the classes. Our results refer to the basic minimization problem as well as to its extension to transition-based and GFG automata. In some cases, we provide bounds, and in others we provide connections between the different settings. Thus, our results are of practical interest and also improve our understanding of the (still very mysterious) minimization problem.
|Original language||American English|
|Title of host publication||Automated Technology for Verification and Analysis - 20th International Symposium, ATVA 2022, Proceedings|
|Editors||Ahmed Bouajjani, Lukáš Holík, Zhilin Wu|
|Publisher||Springer Science and Business Media Deutschland GmbH|
|Number of pages||17|
|State||Published - 2022|
|Event||20th International Symposium on Automated Technology for Verification and Analysis, ATVA 2022 - Virtual, Online|
Duration: 25 Oct 2022 → 28 Oct 2022
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||20th International Symposium on Automated Technology for Verification and Analysis, ATVA 2022|
|Period||25/10/22 → 28/10/22|
Bibliographical noteFunding Information:
Supported by The Neubauer Foundation of Ph.D Fellowship.
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
- Automata on infinite words
- Good-for-games automata