Closure Certificates
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916147056607232 |
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| author | Murali, Vishnu Trivedi, Ashutosh Zamani, Majid |
| author_facet | Murali, Vishnu Trivedi, Ashutosh Zamani, Majid |
| contents | A barrier certificate, defined over the states of a dynamical system, is a real-valued function whose zero level set characterizes an inductively verifiable state invariant separating reachable states from unsafe ones. When combined with powerful decision procedures such as sum-of-squares programming (SOS) or satisfiability-modulo-theory solvers (SMT) barrier certificates enable an automated deductive verification approach to safety. The barrier certificate approach has been extended to refute omega-regular specifications by separating consecutive transitions of omega-automata in the hope of denying all accepting runs. Unsurprisingly, such tactics are bound to be conservative as refutation of recurrence properties requires reasoning about the well-foundedness of the transitive closure of the transition relation. This paper introduces the notion of closure certificates as a natural extension of barrier certificates from state invariants to transition invariants. We provide SOS and SMT based characterization for automating the search of closure certificates and demonstrate their effectiveness via a paradigmatic case study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_17519 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Closure Certificates Murali, Vishnu Trivedi, Ashutosh Zamani, Majid Logic in Computer Science Systems and Control A barrier certificate, defined over the states of a dynamical system, is a real-valued function whose zero level set characterizes an inductively verifiable state invariant separating reachable states from unsafe ones. When combined with powerful decision procedures such as sum-of-squares programming (SOS) or satisfiability-modulo-theory solvers (SMT) barrier certificates enable an automated deductive verification approach to safety. The barrier certificate approach has been extended to refute omega-regular specifications by separating consecutive transitions of omega-automata in the hope of denying all accepting runs. Unsurprisingly, such tactics are bound to be conservative as refutation of recurrence properties requires reasoning about the well-foundedness of the transitive closure of the transition relation. This paper introduces the notion of closure certificates as a natural extension of barrier certificates from state invariants to transition invariants. We provide SOS and SMT based characterization for automating the search of closure certificates and demonstrate their effectiveness via a paradigmatic case study. |
| title | Closure Certificates |
| topic | Logic in Computer Science Systems and Control |
| url | https://arxiv.org/abs/2305.17519 |