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Synchronized CTL over One-Counter Automata

Authors Shaull Almagor , Daniel Assa, Udi Boker

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ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • CTL
  • Synchronization
  • One Counter Automata
  • Model Checking

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Abstract

We consider the model-checking problem of Synchronized Computation-Tree Logic (CTL+Sync) over One-Counter Automata (OCAs). CTL+Sync augments CTL with temporal operators that require several paths to satisfy properties in a synchronous manner, e.g., the property "all paths should eventually see p at the same time". The model-checking problem for CTL+Sync over finite-state Kripke structures was shown to be in 𝖯^{NP^NP}. OCAs are labelled transition systems equipped with a non-negative counter that can be zero-tested. Thus, they induce infinite-state systems whose computation trees are not regular. The model-checking problem for CTL over OCAs was shown to be PSPACE-complete. 
We show that the model-checking problem for CTL+Sync over OCAs is decidable. However, the upper bound we give is non-elementary. We therefore proceed to study the problem for a central fragment of CTL+Sync, extending CTL with operators that require all paths to satisfy properties in a synchronous manner, and show that it is in EXP^NEXP (and in particular in EXPSPACE), by exhibiting a certain "segmented periodicity" in the computation trees of OCAs.

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Shaull Almagor, Daniel Assa, and Udi Boker. Synchronized CTL over One-Counter Automata. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 19:1-19:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.FSTTCS.2023.19

Author Details

Shaull Almagor
  • Department of Computer Science, Technion, Israel
Daniel Assa
  • Reichman University, Herzliya, Israel
Udi Boker
  • Reichman University, Herzliya, Israel

Funding

  • Almagor, Shaull: supported by the Israel Science Foundation grant 989/22.
  • Boker, Udi: supported by the Israel Science Foundation grant 2410/22.

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