Polynomial-Time Verification of PCTL Properties of MDPs with Convex Uncertainties

Puggelli, Alberto; Li, Wenchao; Sangiovanni‐Vincentelli, Alberto; Seshia, Sanjit A.

doi:10.21236/ada583813

Cited by 42 publications

(65 citation statements)

References 4 publications

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“…PCTL model checking of IMCs accommodates the optimization strategy involved in PCTL model checking of IMCs. Puggelli et al [24] presented a method based on convex programming for PCTL model checking of MDPs and showed that the computational time bound is pseudo-polynomial. By contrast, Benedikt et al [5] considered the LTL model checking problem for IMCs, which they defined as the search for an MC belonging to an IMC such that probability of satisfying an LTL formula is optimal.…”

Section: Related Workmentioning

confidence: 99%

Perturbation analysis of stochastic systems with empirical distribution parameters

Rosenblum

2014

Proceedings of the 36th International Conference on Software Engineering

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Probabilistic model checking is a quantitative verification technology for computer systems and has been the focus of intense research for over a decade. While in many circumstances of probabilistic model checking it is reasonable to anticipate a possible discrepancy between a stochastic model and a real-world system it represents, the state-of-the-art provides little account for the effects of this discrepancy on verification results. To address this problem, we present a perturbation approach in which quantities such as transition probabilities in the stochastic model are allowed to be perturbed from their measured values. We present a rigorous mathematical characterization for variations that can occur to verification results in the presence of model perturbations. The formal treatment is based on the analysis of a parametric variant of discrete-time Markov chains, called parametric Markov chains (PMCs), which are equipped with a metric to measure their perturbed vector variables. We employ an asymptotic method from perturbation theory to compute two forms of perturbation bounds, namely condition numbers and quadratic bounds, for automata-based verification of PMCs. We also evaluate our approach with case studies on variant models for three widely studied systems, the Zeroconf protocol, the Leader Election Protocol and the NAND Multiplexer.

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Section: Related Workmentioning

confidence: 99%

Perturbation analysis of stochastic systems with empirical distribution parameters

Rosenblum

2014

Proceedings of the 36th International Conference on Software Engineering

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“…Therefore, in this case we infer a generalization of an MDP called a Convex-MDP (CMDP) [17], where the uncertainty in the values of transition probabilities is captured in the form of convex uncertainty regions, a first-class component of the model. Puggelli et al [17] show how one can extend algorithms for model checking properties expressed in probabilistic computation tree logic (PCTL) to the CMDP model. Sadigh et al [19] use that model to infer desired properties about human driver behavior, such as a quantitative evaluation of distracted driving.…”

Section: Environment Estimationmentioning

confidence: 99%

Formal methods for semi-autonomous driving

Seshia

Sadigh

Sastry

2015

Proceedings of the 52nd Annual Design Automation Conference

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“…Such a construction results in an exponential blow up, which is also not avoided in [5] for qualitative proper-ties (when transitions can have 0 as their left endpoint). [6,17] improve on these results to present polynomial-time algorithms for reachability problems based on linear or convex programming. The paper [12] includes polynomial-time methods for computing (maximal) end components, and for computing a single step of value iteration, for interval MDPs.…”

Section: Introductionmentioning

confidence: 98%

Qualitative Reachability for Open Interval Markov Chains

Sproston

2018

Lecture Notes in Computer Science

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Interval Markov chains extend classical Markov chains with the possibility to describe transition probabilities using intervals, rather than exact values. While the standard formulation of interval Markov chains features closed intervals, previous work has considered also open interval Markov chains, in which the intervals can also be open or halfopen.In this paper we focus on qualitative reachability problems for open interval Markov chains, which consider whether the optimal (maximum or minimum) probability with which a certain set of states can be reached is equal to 0 or 1. We present polynomial-time algorithms for these problems for both of the standard semantics of interval Markov chains. Our methods do not rely on the closure of open intervals, in contrast to previous approaches for open interval Markov chains, and can characterise situations in which probability 0 or 1 can be attained not exactly but arbitrarily closely.

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Polynomial-Time Verification of PCTL Properties of MDPs with Convex Uncertainties

Cited by 42 publications

References 4 publications

Perturbation analysis of stochastic systems with empirical distribution parameters

Perturbation analysis of stochastic systems with empirical distribution parameters

Formal methods for semi-autonomous driving

Qualitative Reachability for Open Interval Markov Chains

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