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Resolving Nondeterminism with Randomness

Authors Thomas A. Henzinger , Aditya Prakash , K. S. Thejaswini

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ACM Subject Classification
  • Theory of computation → Automata over infinite objects
Keywords
  • ω-regular languages
  • History determinism
  • Stochastic strategies

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Abstract

We define and study classes of ω-regular automata for which the nondeterminism can be resolved by a policy that uses a combination of memory and randomness on any input word, based solely on the prefix read so far. We examine two settings for providing the input word to an automaton. In the first setting, called adversarial resolvability, the input word is constructed letter-by-letter by an adversary, dependent on the resolver’s previous decisions. In the second setting, called stochastic resolvability, the adversary pre-commits to an infinite word and reveals it letter-by-letter. In each setting, we require the existence of an almost-sure resolver, i.e., a policy that ensures that as long as the adversary provides a word in the language of the underlying nondeterministic automaton, the run constructed by the policy is accepting with probability 1.
The class of automata that are adversarially resolvable is the well-studied class of history-deterministic automata. The case of stochastically resolvable automata, on the other hand, defines a novel class. Restricting the class of resolvers in both settings to stochastic policies without memory introduces two additional new classes of automata. We show that the new automata classes offer interesting trade-offs between succinctness, expressivity, and computational complexity, providing a fine gradation between deterministic automata and nondeterministic automata.

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Thomas A. Henzinger, Aditya Prakash, and K. S. Thejaswini. Resolving Nondeterminism with Randomness. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 57:1-57:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.57

Author Details

Thomas A. Henzinger
  • Institute of Science and Technology Austria, Klosterneuburg, Austria
Aditya Prakash
  • University of Warwick, UK
  • LIS, Aix-Marseille Université, France
K. S. Thejaswini
  • Institute of Science and Technology Austria, Klosterneuburg, Austria

Funding

This work is a part of project VAMOS that has received funding from the European Research Council (ERC), grant agreement No 101020093.

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