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Speed Me up If You Can: Conditional Lower Bounds on Opacity Verification

Authors Jiří Balun , Tomáš Masopust , Petr Osička

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Author Details

Jiří Balun
  • Faculty of Science, Palacky University Olomouc, Czech Republic
Tomáš Masopust
  • Faculty of Science, Palacky University Olomouc, Czech Republic
Petr Osička
  • Faculty of Science, Palacky University Olomouc, Czech Republic

Funding

  • Balun, Jiří: Supported by IGA PrF 2023 026.

Acknowledgements

We acknowledge valuable comments and suggestions of anonymous referees.

Cite AsGet BibTex

Jiří Balun, Tomáš Masopust, and Petr Osička. Speed Me up If You Can: Conditional Lower Bounds on Opacity Verification. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.MFCS.2023.16

Abstract

Opacity is a property of privacy and security applications asking whether, given a system model, a passive intruder that makes online observations of system’s behaviour can ascertain some "secret" information of the system. Deciding opacity is a PSpace-complete problem, and hence there are no polynomial-time algorithms to verify opacity under the assumption that PSpace differs from PTime. This assumption, however, gives rise to a question whether the existing exponential-time algorithms are the best possible or whether there are faster, sub-exponential-time algorithms. We show that under the (Strong) Exponential Time Hypothesis, there are no algorithms that would be significantly faster than the existing algorithms. As a by-product, we obtained a new conditional lower bound on the time complexity of deciding universality (and therefore also inclusion and equivalence) for nondeterministic finite automata.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Finite automata
  • opacity
  • fine-grained complexity

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