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In order to facilitate automated reasoning about large Boolean combinations of nonlinear 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)

- Christian Herde, Andreas Eggers, Martin Fränzle, Tino Teige
- ICONS
- 2008

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)

- Martin Fränzle, Tino Teige, Andreas Eggers
- J. Log. Algebr. Program.
- 2010

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)

- Bahareh Badban, Martin Fränzle, Jan Peleska, Tino Teige
- SOQUA
- 2006

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)

- Martin Fränzle, Holger Hermanns, Tino Teige
- HSCC
- 2008

The analysis of hybrid systems exhibiting probabilistic behaviour is notoriously difficult. To enable mechanised 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)

- Tino Teige
- 2012

In today’s high-tech world, embedded computer systems interacting with technical, physical, or even biological environments are our permanent companions. While several of these applications are almost free of risk and just contribute to a better quality of life such as the use of cellular phones, washing machines, and refrigerators, other embedded systems… (More)

In previous publications, the authors have introduced the notion of stochastic satisfiability modulo theories (SSMT) and the corresponding SiSAT solving algorithm, which provide a symbolic method for the reachability analysis of probabilistic hybrid systems. SSMT extends satisfiability modulo theories (SMT) with randomized (or stochastic), existential, and… (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)

- Stefan Kupferschmid, Bernd Becker, Tino Teige, Martin Fränzle
- DDECS
- 2011

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 safetycritical 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)

- Andreas Eggers, Natalia Kalinnik, Stefan Kupferschmid, Tino Teige
- CSCLP
- 2008

In the analysis of hybrid discrete-continuous systems, rich arithmetic constraint formulae with complex Boolean structure arise naturally. The iSAT algorithm, a solver for such formulae, is aimed at bounded model checking of hybrid systems. In this paper, we identify challenges emerging from planned and ongoing work to enhance the iSAT algorithm: First, we… (More)