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Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties

Authors Laura Bozzelli, Adriano Peron, César Sánchez

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LIPIcs.CONCUR.2022.27.pdf
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Author Details

Laura Bozzelli
  • University of Napoli "Federico II", Italy
Adriano Peron
  • University of Napoli "Federico II", Italy
César Sánchez
  • IMDEA Software Institute, Madrid, Spain

Funding

  • Sánchez, César: funded in part by the Madrid Regional Government under project "S2018/TCS-4339 (BLOQUES-CM)" and by a research grant from Nomadic Labs and the Tezos Foundation.

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Laura Bozzelli, Adriano Peron, and César Sánchez. Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CONCUR.2022.27

Abstract

Hyperproperties are properties of systems that relate different executions traces, with many applications from security to symmetry, consistency models of concurrency, etc. In recent years, different linear-time logics for specifying asynchronous hyperproperties have been investigated. Though model checking of these logics is undecidable, useful decidable fragments have been identified with applications e.g. for asynchronous security analysis. In this paper, we address expressiveness and decidability issues of temporal logics for asynchronous hyperproperties. We compare the expressiveness of these logics together with the extension S1S[E] of S1S with the equal-level predicate by obtaining an almost complete expressiveness picture. We also study the expressive power of these logics when interpreted on singleton sets of traces. We show that for two asynchronous extensions of HyperLTL, checking the existence of a singleton model is already undecidable, and for one of them, namely Context HyperLTL (HyperLTL_C), we establish a characterization of the singleton models in terms of the extension of standard FO[<] over traces with addition. This last result generalizes the well-known equivalence between FO[<] and LTL. Finally, we identify new boundaries on the decidability of model checking HyperLTL_C.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
Keywords
  • Hyperproperties
  • Asynchronous hyperproperties
  • Temporal logics for hyperproperties
  • Expressiveness
  • Decidability
  • Model checking

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