Minimal counterexamples for linear-time probabilistic verification

Wimmer, Ralf; Jansen, Nils; Ábrahám, Erika; Katoen, Joost-Pieter; Becker, Bernd

doi:10.1016/j.tcs.2014.06.020

Cited by 29 publications

(39 citation statements)

References 20 publications

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“…Witnessing subsystems in MDPs have been considered in [6,9] and [19], which focuses on succinctly representing witnessing schedulers. The mixed integer linear programming (MILP) formulation of [76,77] allows for an exact computation of minimal witnessing subsystems for the property Pr max s0 (♦ goal) λ. NPcompleteness of computing minimal witnessing subsystems in MDPs was shown in [23], but the exact complexity has, to the best of our knowledge, not been determined for DTMCs (the problem was conjectured to be NP-complete in [76]).…”

Section: Property Certificate Dimension Certificate Conditionmentioning

confidence: 99%

“…Subsystems, witnesses and notions of minimality. Our definition of subsystem is essentially the same to the definition in [76,77] Intuitively, a subsystem M of M contains a subset of states of M, and a transition of M originating in a state of M remains unchanged in M or is redirected to fail (instead of explicitely redirecting to fail, sub-stochastic distributions are used in [76,77] with the same effect). We say that the states S all \S all and the transitions (s, α, t) with P(s, α, t) > 0 and P (s, α, t) = 0 have been deleted in M .…”

Section: Minimal Witnesses For Reachability In Mdpsmentioning

confidence: 99%

“…In this section we determine the computational complexity of the witness problem: Given a DTMC M, a positive integer k, and a rational number λ ∈ [0, 1], decide whether there exists a witness M ⊆ M for Pr M,s0 (♦ goal) ≥ λ with at most k states. The corresponding problem for MDPs is known to be NPcomplete [23,77] 1 . In this section we show that the witness problem is even NP-complete for acyclic DTMCs, where acyclicity means that the underlying graph with V = S and E = {(s, t) ∈ S × S | P(s, t) > 0} is acyclic (as before, we take S = S all \{goal, fail}).…”

Section: Minimal Witnesses For Reachability In Mdpsmentioning

confidence: 99%

“…Mixed integer linear programming. An approach that computes minimal witnesses to the threshold problem Pr max s0 (♦ goal) ≥ λ using mixed integer linear programs (MILP) was presented in [76,77]. Using the following lemma, we can derive MILP formulations from our polytope formulations.…”

Section: Computing Witnessing Subsystemsmentioning

confidence: 99%

See 3 more Smart Citations

Farkas Certificates and Minimal Witnesses for Probabilistic Reachability Constraints

Funke

Jantsch

Baier

2020

Tools and Algorithms for the Construction and Analysis of Systems

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This paper introduces Farkas certificates for lower and upper bounds on minimal and maximal reachability probabilities in Markov decision processes (MDP), which we derive using an MDP-variant of Farkas' Lemma. The set of all such certificates is shown to form a polytope whose points correspond to witnessing subsystems of the model and the property. This allows translating the problem of finding minimal witnesses to the problem of finding vertices with a maximal number of zeros. While computing such vertices is computationally hard in general, we derive new heuristics from our formulations that exhibit competitive performance compared to state-of-the-art techniques and apply to more situations. As an argument that asymptotically better algorithms cannot be hoped for, we show that the decision version of finding minimal witnesses is NP-complete even for acyclic Markov chains.

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Section: Property Certificate Dimension Certificate Conditionmentioning

confidence: 99%

Section: Minimal Witnesses For Reachability In Mdpsmentioning

confidence: 99%

Section: Minimal Witnesses For Reachability In Mdpsmentioning

confidence: 99%

Section: Computing Witnessing Subsystemsmentioning

confidence: 99%

See 2 more Smart Citations

Farkas Certificates and Minimal Witnesses for Probabilistic Reachability Constraints

Funke

Jantsch

Baier

2020

Tools and Algorithms for the Construction and Analysis of Systems

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“…An alternative would be to use an MILP encoding like, e. g., in [11,19], and optimize towards a maximal number of available nondeterministic choices. However, in our setting it is crucial to ensure incrementality in the sense that if certain changes to the constraints are necessary this does not trigger a complete restart of the solving process.…”

Section: Computing Permissive Schedulersmentioning

confidence: 99%

Safety-Constrained Reinforcement Learning for MDPs

Junges

Jansen

Dehnert

et al. 2016

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. We consider controller synthesis for stochastic and partially unknown environments in which safety is essential. Specifically, we abstract the problem as a Markov decision process in which the expected performance is measured using a cost function that is unknown prior to run-time exploration of the state space. Standard learning approaches synthesize cost-optimal strategies without guaranteeing safety properties. To remedy this, we first compute safe, permissive strategies. Then, exploration is constrained to these strategies and thereby meets the imposed safety requirements. Exploiting an iterative learning procedure, the resulting policy is safety-constrained and optimal. We show correctness and completeness of the method and discuss the use of several heuristics to increase its scalability. Finally, we demonstrate the applicability by means of a prototype implementation.

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