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Deductive Controller Synthesis for Probabilistic Hyperproperties

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Quantitative Evaluation of Systems (QEST 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14287))

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Abstract

Probabilistic hyperproperties specify quantitative relations between the probabilities of reaching different target sets of states from different initial sets of states. This class of behavioral properties is suitable for capturing important security, privacy, and system-level requirements. We propose a new approach to solve the controller synthesis problem for Markov decision processes (MDPs) and probabilistic hyperproperties. Our specification language builds on top of the logic HyperPCTL and enhances it with structural constraints over the synthesized controllers. Our approach starts from a family of controllers represented symbolically and defined over the same copy of an MDP. We then introduce an abstraction refinement strategy that can relate multiple computation trees and that we employ to prune the search space deductively. The experimental evaluation demonstrates that the proposed approach considerably outperforms HyperProb, a state-of-the-art SMT-based model checking tool for HyperPCTL. Moreover, our approach is the first one that is able to effectively combine probabilistic hyperproperties with additional intra-controller constraints (e.g. partial observability) as well as inter-controller constraints (e.g. agreements on a common action).

This work has been supported by the Czech Science Foundation grant GA23-06963S (VESCAA), the Czech Ministry of Education, Youth and Sports project LL1908 of the ERC.CZ programme, the Vienna Science and Technology Fund 10.47379/ICT19018, and by the European Union’s ERC CoG ARTIST 101002685 grant and the Horizon 2020 research and innovation programme under grant no. 101034440 .

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Notes

  1. 1.

    A verification problem defined using universal quantification can be treated as synthesis of a counterexample. Alternation in the controller quantification is not supported as it principally complicates the inductive synthesis strategy. To the best of our knowledge, only very few techniques so far practically support alternation [13, 30].

  2. 2.

    An extension to nested-free PCTL path formulae is straightforward. Principally, we can extend the probability constraints to allow more complicated expressions (e.g. sum/difference of reachability probabilities from different states) eventually requiring reasoning about more than two computation trees.

  3. 3.

    Case (5), when \(\sigma \) is consistent but incompatible with another controller \(\sigma '\), is handled analogously, as well as when they are inter-controller inconsistent.

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Authors and Affiliations

  1. Brno University of Technology, Brno, Czech Republic

    Roman Andriushchenko & Milan Češka

  2. TU Wien, Wien, Austria

    Ezio Bartocci, Francesco Pontiggia & Sarah Sallinger

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  1. Roman Andriushchenko
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  2. Ezio Bartocci
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  3. Milan Češka
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  4. Francesco Pontiggia
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  5. Sarah Sallinger
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Correspondence to Milan Češka or Francesco Pontiggia .

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Editors and Affiliations

  1. Radboud University Nijmegen, Nijmegen, The Netherlands

    Nils Jansen

  2. IMT Lucca, Lucca, Italy

    Mirco Tribastone

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Andriushchenko, R., Bartocci, E., Češka, M., Pontiggia, F., Sallinger, S. (2023). Deductive Controller Synthesis for Probabilistic Hyperproperties. In: Jansen, N., Tribastone, M. (eds) Quantitative Evaluation of Systems. QEST 2023. Lecture Notes in Computer Science, vol 14287. Springer, Cham. https://doi.org/10.1007/978-3-031-43835-6_20

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