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In order to facilitate automated reasoning about large Boolean combinations of non-linear arithmetic constraints involving transcendental functions, we provide a tight integration of recent SAT solving techniques with interval-based arithmetic constraint solving. Our approach deviates substantially from lazy theorem proving approaches in that it directly… (More)

This article presents novel results on automated test generation for hybrid control systems, which involves the generation of both discrete and real-valued, potentially time-continuous, input data to the system under test. Our generation techniques are allocated in two layers: The upper layer contains a symbolic test case generator constructing test cases… (More)

The analysis of hybrid systems exhibiting probabilistic behaviour is notoriously difficult. To enable mech-anised analysis of such systems, we extend the reasoning power of arithmetic satisfiability-modulo-theory solving (SMT) by a comprehensive treatment of randomized (a.k.a. stochastic) quantification over discrete variables within the mixed… (More)

In this paper we describe the complete workflow of analyzing the dynamic behavior of safety-critical embedded systems with HySAT. HySAT is an arithmetic constraint solver with a tightly integrated bounded model checker for hybrid discrete-continuous systems which — in contrast to many other solvers — is not confined to linear arithmetic, but can also deal… (More)

In this article, we recall different approaches to the constraint-based, symbolic analysis of hybrid discrete-continuous systems and combine them to a technology able to address hybrid systems exhibiting both non-deterministic and probabilistic behavior akin to infinite-state Markov decision processes. To enable mechanized analysis of such systems, we… (More)

The stochastic Boolean satisfiability (SSAT) problem has been introduced by Papadimitriou in 1985 when adding a probabilistic model of uncertainty to propo-sitional satisfiability through randomized quantification. SSAT has many applications, among them probabilistic bounded model checking (PBMC) of symbolically represented Markov decision processes. This… (More)

—Symbolic methods in computer-aided verification rely heavily on constraint solvers. The correctness and reliability of these solvers are of vital importance in the analysis of safety-critical systems, e.g., in the automotive context. Satisfiability results of a solver can usually be checked by probing the computed solution. This is in general not the case… (More)

The first-order theory over non-linear arithmetic including transcendental functions (NLA) is undecidable. Nevertheless, in this paper we show that a particular combination with superposition leads to a sound and complete calculus that is useful in practice. We follow basically the ideas of the SUP(LA) combination, but have to take care of undecidability,… (More)

Stochastic satisfiability modulo theories (SSMT), which is an extension of satisfiability modulo theories with randomized quantifi-cation, has successfully been used as a symbolic technique for computing reachability probabilities in probabilistic hybrid systems. Motivated by the fact that several industrial applications call for quantitative measures that… (More)