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Randomization in Non-Uniform Finite Automata

Authors Pavol Ďuriš, Rastislav Královič, Richard Královič, Dana Pardubská, Martin Pašen, Peter Rossmanith

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Subject Classification

ACM Subject Classification
  • Theory of computation → Automata extensions
Keywords
  • finite automata
  • non-uniform computation
  • randomization

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Abstract

The non-uniform version of Turing machines with an extra advice input tape that depends on the length of the input but not the input itself is a well-studied model in complexity theory. We investigate the same notion of non-uniformity in weaker models, namely one-way finite automata. In particular, we are interested in the power of two-sided bounded-error randomization, and how it compares to determinism and non-determinism. We show that for unlimited advice, randomization is strictly stronger than determinism, and strictly weaker than non-determinism. However, when the advice is restricted to polynomial length, the landscape changes: the expressive power of determinism and randomization does not change, but the power of non-determinism is reduced to the extent that it becomes incomparable with randomization.

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Pavol Ďuriš, Rastislav Královič, Richard Královič, Dana Pardubská, Martin Pašen, and Peter Rossmanith. Randomization in Non-Uniform Finite Automata. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 30:1-30:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.MFCS.2020.30

Author Details

Pavol Ďuriš
  • Comenius University in Bratislava, Slovakia
Rastislav Královič
  • Comenius University in Bratislava, Slovakia
Richard Královič
  • Google Inc., Zürich, Switzerland
Dana Pardubská
  • Comenius University in Bratislava, Slovakia
Martin Pašen
  • Comenius University in Bratislava, Slovakia
Peter Rossmanith
  • RWTH Aachen, Germany

Funding

This research has been partially supported by the grant 1 20 of the Slovak Scientific Grant Agency VEGA.

References

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