License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2020.30
URN: urn:nbn:de:0030-drops-126987
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12698/
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Ďuriš, Pavol ; Královič, Rastislav ; Královič, Richard ; Pardubská, Dana ; Pašen, Martin ; Rossmanith, Peter

Randomization in Non-Uniform Finite Automata

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LIPIcs-MFCS-2020-30.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{uri_et_al:LIPIcs:2020:12698,
  author =	{Pavol Ďuri{\v{s}} and Rastislav Kr{\'a}lovič and Richard Kr{\'a}lovič and Dana Pardubsk{\'a} and Martin Pa{\v{s}}en and Peter Rossmanith},
  title =	{{Randomization in Non-Uniform Finite Automata}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{30:1--30:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Javier Esparza and Daniel Kr{\'a}ľ},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12698},
  URN =		{urn:nbn:de:0030-drops-126987},
  doi =		{10.4230/LIPIcs.MFCS.2020.30},
  annote =	{Keywords: finite automata, non-uniform computation, randomization}
}

Keywords: finite automata, non-uniform computation, randomization
Collection: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Issue Date: 2020
Date of publication: 18.08.2020

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