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Strategic Dominance: A New Preorder for Nondeterministic Processes

Authors Thomas A. Henzinger , Nicolas Mazzocchi , N. Ege Saraç

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Author Details

Thomas A. Henzinger
  • Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria
Nicolas Mazzocchi
  • Slovak University of Technology in Bratislava, Slovak Republic
  • Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria
N. Ege Saraç
  • Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria

Funding

This work was supported in part by the ERC-2020-AdG 101020093. N. Mazzocchi was affiliated with ISTA when this work was submitted for publication.

Acknowledgements

We thank the anonymous reviewers for their helpful comments.

Cite As Get BibTex

Thomas A. Henzinger, Nicolas Mazzocchi, and N. Ege Saraç. Strategic Dominance: A New Preorder for Nondeterministic Processes. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CONCUR.2024.29

Abstract

We study the following refinement relation between nondeterministic state-transition models: model ℬ strategically dominates model 𝒜 iff every deterministic refinement of 𝒜 is language contained in some deterministic refinement of ℬ. While language containment is trace inclusion, and the (fair) simulation preorder coincides with tree inclusion, strategic dominance falls strictly between the two and can be characterized as "strategy inclusion" between 𝒜 and ℬ: every strategy that resolves the nondeterminism of 𝒜 is dominated by a strategy that resolves the nondeterminism of ℬ. Strategic dominance can be checked in 2-ExpTime by a decidable first-order Presburger logic with quantification over words and strategies, called resolver logic. We give several other applications of resolver logic, including checking the co-safety, co-liveness, and history-determinism of boolean and quantitative automata, and checking the inclusion between hyperproperties that are specified by nondeterministic boolean and quantitative automata.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Logic and verification
  • Theory of computation → Program reasoning
Keywords
  • quantitative automata
  • refinement relation
  • resolver
  • strategy
  • history-determinism

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