Exact quantitative probabilistic model checking through rational search

Bauer, Matthew S.; Mathur, Umang; Chadha, Rohit; Sistla, A. Prasad; Viswanathan, Mahesh

doi:10.23919/fmcad.2017.8102246

Cited by 10 publications

(11 citation statements)

References 28 publications

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“…Exact computations are handled in e.g. [17,18] For the sake of clarity, we focus on reachability probabilities and sketch how the techniques can be lifted to expected rewards.…”

Section: Probabilistic Model Checking Via Interval Iterationmentioning

confidence: 99%

Sound Value Iteration

Quatmann

Katoen

2018

Computer Aided Verification

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Abstract. Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by determining reachability probabilities for an increasing number of steps. To avoid results that are significantly off, variants have recently been proposed that converge from both below and above. These procedures require starting values for both sides. We present an alternative that does not require the a priori computation of starting vectors and that converges faster on many benchmarks. The crux of our technique is to give tight and safe bounds-whose computation is cheap-on the reachability probabilities. Lifting this technique to expected rewards is trivial for both Markov chains and MDPs. Experimental results on a large set of benchmarks show its scalability and efficiency.

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“…Exact computations are handled in e.g. [17,18] For the sake of clarity, we focus on reachability probabilities and sketch how the techniques can be lifted to expected rewards.…”

Section: Probabilistic Model Checking Via Interval Iterationmentioning

confidence: 99%

Sound Value Iteration

Quatmann

Katoen

2018

Computer Aided Verification

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“…-offers the possibility to improve the reliability of model checking by supporting exact rational arithmetic using recent techniques [18] and techniques to avoid premature termination of value iteration [110]. -supports advanced properties such as multi-objective model checking [51,52,109], efficient algorithms for conditional probabilities and rewards [13], and long-run averages on MDPs [6,44] and MAs [28].…”

Section: Storm In a Nutshellmentioning

confidence: 99%

“…Several works [18,58,121,123] observed that the numerical methods applied by probabilistic model checkers are prone to numerical errors. This has mostly two reasons.…”

Section: Exact and Sound Model Checkingmentioning

confidence: 99%

“…Storm offers two tailored techniques to solve systems of (in)equations using rational arithmetic. The first is based on policy iteration and Gaussian elimination and the second on a recent technique called rational search [18]. The idea of the latter is to use an (imprecise) approximation of the exact solution and then sharpen this to a precise rational solution using the Kwek-Mehlhorn algorithm [90].…”

Section: Exact and Sound Model Checkingmentioning

confidence: 99%

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The probabilistic model checker Storm

Hensel

Junges

Katoen

et al. 2021

Int J Softw Tools Technol Transfer

115

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We present the probabilistic model checker Storm. Storm supports the analysis of discrete- and continuous-time variants of both Markov chains and Markov decision processes. Storm has three major distinguishing features. It supports multiple input languages for Markov models, including the Jani and Prism modeling languages, dynamic fault trees, generalized stochastic Petri nets, and the probabilistic guarded command language. It has a modular setup in which solvers and symbolic engines can easily be exchanged. Its Python API allows for rapid prototyping by encapsulating Storm’s fast and scalable algorithms. This paper reports on the main features of Storm and explains how to effectively use them. A description is provided of the main distinguishing functionalities of Storm. Finally, an empirical evaluation of different configurations of Storm on the QComp 2019 benchmark set is presented.

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“…The only known convergence criterion for pure VI was presented in [9, Sect. 3.5]: if we run VI until the absolute error between two iterations is less than a certain value α, then the computed values at that point are within α of the true values, and can in fact be rounded to the exact true values (as implemented in the rational search approach [5]). However, α cannot be freely chosen; it is a fixed number that depends on the size of the MDP and the largest denominator of the (rational) transition probabilities.…”

Section: Introductionmentioning

confidence: 99%

Optimistic Value Iteration

Hartmanns

Kaminski

2020

Lecture Notes in Computer Science

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Markov decision processes are widely used for planning and verification in settings that combine controllable or adversarial choices with probabilistic behaviour. The standard analysis algorithm, value iteration, only provides lower bounds on infinite-horizon probabilities and rewards. Two "sound" variations, which also deliver an upper bound, have recently appeared. In this paper, we present a new sound approach that leverages value iteration's ability to usually deliver good lower bounds: we obtain a lower bound via standard value iteration, use the result to "guess" an upper bound, and prove the latter's correctness. We present this optimistic value iteration approach for computing reachability probabilities as well as expected rewards. It is easy to implement and performs well, as we show via an extensive experimental evaluation using our implementation within the mcsta model checker of the Modest Toolset.

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Exact quantitative probabilistic model checking through rational search

Cited by 10 publications

References 28 publications

Sound Value Iteration

Sound Value Iteration

The probabilistic model checker Storm

Optimistic Value Iteration

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