Abstract
Stochastic Satisfiability Modulo Theories (SSMT) [1] is a quantitative extension of classical Satisfiability Modulo Theories (SMT) inspired by stochastic logics. It extends SMT by the usual as well as randomized quantifiers, facilitating capture of stochastic game properties in the logic, like reachability analysis of hybrid-state Markov decision processes. Solving for SSMT formulae with quantification over finite and thus discrete domain has been addressed by Tino Teige et al. [2]. In this paper, we extend their work to SSMT over continuous quantifier domains (CSSMT) in order to enable capture of continuous disturbances and uncertainty in hybrid systems. We extend the semantics of SSMT and introduce a corresponding solving procedure. A simple case study is pursued to demonstrate applicability of our framework to reachability problems in hybrid systems.
This research is funded by the German Research Foundation through the Research Training Group DFG-GRK 1765: “System Correctness under Adverse Conditions” (SCARE, scare.uni-oldenburg.de) and the Transregional Collaborative Research Center SFB-TR 14 “Automatic Verification and Analysis of Complex Systems” (AVACS, www.avacs.org).
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Notes
- 1.
In SSAT parlance, this is the body of the formula after rewriting it to prenex form and stripping all the quantifiers.
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Gao, Y., Fränzle, M. (2015). A Solving Procedure for Stochastic Satisfiability Modulo Theories with Continuous Domain. In: Campos, J., Haverkort, B. (eds) Quantitative Evaluation of Systems. QEST 2015. Lecture Notes in Computer Science(), vol 9259. Springer, Cham. https://doi.org/10.1007/978-3-319-22264-6_19
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