Stochastic Satisfiability Modulo Theory: A Novel Technique for the Analysis of Probabilistic Hybrid Systems

Fränzle, Martin; Hermanns, Holger; Teige, Tino

doi:10.1007/978-3-540-78929-1_13

Cited by 63 publications

(58 citation statements)

References 20 publications

(38 reference statements)

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“…As a modeling framework to deal with uncertainties, we consider probabilistic hybrid automata (PHA, cf. [19]) which extends the notion of hybrid automata s.t. the non-deterministic selection of a transition is enriched by a probabilistic choice according to a distribution over variants of the transition.…”

Section: Stochastic Constraint Systemsmentioning

confidence: 99%

“…1, where T , f cool , and t denote the temperature, the cooling factor, and the time, resp., and ∆t is the discretization parameter. In order to automatically compute the reachability probability of (un-)desired properties of PHAs, in [19] we introduced stochastic satisfiability modulo theories (SSMT) as the unification of stochastic propositional satisfiability (SSAT) [30] and satisfiability modulo theories (SMT, e.g. [32]).…”

Section: Stochastic Constraint Systemsmentioning

confidence: 99%

“…The solution of an SSMT problem Φ is a tree of assignments to the existential variables that maximizes the overall satisfaction probability of Φ (cf. [19] for more details). In our application, we are interested in computing the maximum probability of satisfaction.…”

Section: Stochastic Constraint Systemsmentioning

confidence: 99%

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Challenges in Constraint-Based Analysis of Hybrid Systems

Eggers

Kalinnik

Kupferschmid

et al. 2009

Lecture Notes in Computer Science

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Abstract. 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 propose an extension of iSAT to directly handle ordinary differential equations as constraints. Second, we outline the recently introduced generalization of the iSAT algorithm to deal with probabilistic hybrid systems and some open research issues in that context. Third, we present ideas on how to move from bounded to unbounded model checking by using the concept of interpolation. Finally, we discuss the adaption of some parallelization techniques to the iSAT case, which will hopefully lead to performance gains in the future. By presenting these open research questions, this paper aims at fostering discussions on these extensions of constraint solving.

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Section: Stochastic Constraint Systemsmentioning

confidence: 99%

Section: Stochastic Constraint Systemsmentioning

confidence: 99%

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Challenges in Constraint-Based Analysis of Hybrid Systems

Eggers

Kalinnik

Kupferschmid

et al. 2009

Lecture Notes in Computer Science

Self Cite

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“…Formal definitions of various classes of continuous-time probabilistic hybrid models are presented in [28], together with a comparison. Over such models, [5] has formalized the notion of probabilistic reachability, [29] has proposed a computational technique based on convex optimization, [14] has provided discretization techniques with formal error bounds, and [15] has developed an approach based on satisfiability modulo theory. An alternative approach towards formal, finite approximations of continuous-time stochastic models is discussed in [35] and extended in [34] to switching diffusions.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Monte Carlo Method for Statistical Model Checking of Hybrid Systems

Soudjani

Majumdar

Nagapetyan

2017

Quantitative Evaluation of Systems

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Abstract. We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo method (MLMC) and work on a sequence of discrete-time stochastic processes whose executions approximate and converge weakly to that of the original continuous-time stochastic hybrid system with respect to satisfaction of the property of interest. With focus on bounded-horizon reachability, we recast the model checking problem as the computation of the distribution of the exit time, which is in turn formulated as the expectation of an indicator function. This latter computation involves estimating discontinuous functionals, which reduces the bound on the convergence rate of the Monte Carlo algorithm. We propose a smoothing step with tunable precision and formally quantify the error of the MLMC approach in the mean-square sense, which is composed of smoothing error, bias, and variance. We formulate a general adaptive algorithm which balances these error terms. Finally, we describe an application of our technique to verify a model of thermostatically controlled loads.

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“…These involve either imposing a grid on the state space, thus turning an infinite state problem into an approximate finite state one (see, for example, [1,32] for reachability problems of the type considered here), or carrying out Monte-Carlo simulations to obtain empirical estimates of quantities such as expected values of reach probabilities (see [27] for an application of such methods). An alternative approach to the problem of verification of stochastic hybrid systems is based on satisfiability modulo theory, [19]. In [31], certain functions of the state are used to determine upper bounds on the invariance probability.…”

Section: Introductionmentioning

confidence: 99%