Interpolation-Inspired Closure Certificates
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917272137760768 |
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| author | Oumer, Mohammed Adib Murali, Vishnu Zamani, Majid |
| author_facet | Oumer, Mohammed Adib Murali, Vishnu Zamani, Majid |
| contents | Barrier certificates, a form of state invariants, provide an automated approach to the verification of the safety of dynamical systems. Similarly to barrier certificates, recent works explore the notion of closure certificates, a form of transition invariants, to verify dynamical systems against $ω$-regular properties including safety. A closure certificate, defined over state pairs of a dynamical system, is a real-valued function whose zero superlevel set characterizes an inductive transition invariant of the system. The search for such a certificate can be effectively automated by assuming it to be within a specific template class, e.g. a polynomial of a fixed degree, and then using optimization techniques such as sum-of-squares (SOS) programming to find it. Unfortunately, one may not be able to find such a certificate for a fixed template. In such a case, one must change the template, e.g. increase the degree of the polynomial. In this paper, we consider a notion of multiple closure certificates dubbed interpolation-inspired closure certificates. An interpolation-inspired closure certificate consists of a set of functions which jointly over-approximate a transition invariant by first considering one-step transitions, then two, and so on until a transition invariant is obtained. The advantage of interpolation-inspired closure certificates is that they allow us to prove properties even when a single function for a fixed template cannot be found using standard approaches. We present SOS programming and a scenario program to find these sets of functions and demonstrate the effectiveness of our proposed method to verify persistence and general $ω$-regular specifications in some case studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12436 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Interpolation-Inspired Closure Certificates Oumer, Mohammed Adib Murali, Vishnu Zamani, Majid Systems and Control Formal Languages and Automata Theory Barrier certificates, a form of state invariants, provide an automated approach to the verification of the safety of dynamical systems. Similarly to barrier certificates, recent works explore the notion of closure certificates, a form of transition invariants, to verify dynamical systems against $ω$-regular properties including safety. A closure certificate, defined over state pairs of a dynamical system, is a real-valued function whose zero superlevel set characterizes an inductive transition invariant of the system. The search for such a certificate can be effectively automated by assuming it to be within a specific template class, e.g. a polynomial of a fixed degree, and then using optimization techniques such as sum-of-squares (SOS) programming to find it. Unfortunately, one may not be able to find such a certificate for a fixed template. In such a case, one must change the template, e.g. increase the degree of the polynomial. In this paper, we consider a notion of multiple closure certificates dubbed interpolation-inspired closure certificates. An interpolation-inspired closure certificate consists of a set of functions which jointly over-approximate a transition invariant by first considering one-step transitions, then two, and so on until a transition invariant is obtained. The advantage of interpolation-inspired closure certificates is that they allow us to prove properties even when a single function for a fixed template cannot be found using standard approaches. We present SOS programming and a scenario program to find these sets of functions and demonstrate the effectiveness of our proposed method to verify persistence and general $ω$-regular specifications in some case studies. |
| title | Interpolation-Inspired Closure Certificates |
| topic | Systems and Control Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2602.12436 |