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

Jiří Balun; Tomáš Masopust; Petr Osička

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arXiv · 2304.09920

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

Jiří Balun·Tomáš Masopust·Petr Osička

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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.

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BibTeX RIS

Jiří Balun, Tomáš Masopust, Petr Osička. 2023-04-19. Speed Me up if You Can: Conditional Lower Bounds on Opacity Verification. https://arxiv.org/abs/2304.09920

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