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.2018.48
URN: urn:nbn:de:0030-drops-96305
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9630/
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Catalano, Costanza ; Jungers, Raphaël M.

On Randomized Generation of Slowly Synchronizing Automata

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LIPIcs-MFCS-2018-48.pdf (0.6 MB)

Abstract

Motivated by the randomized generation of slowly synchronizing automata, we study automata made of permutation letters and a merging letter of rank n-1 . We present a constructive randomized procedure to generate synchronizing automata of that kind with (potentially) large alphabet size based on recent results on primitive sets of matrices. We report numerical results showing that our algorithm finds automata with much larger reset threshold than a mere uniform random generation and we present new families of automata with reset threshold of Omega(n^2/4) . We finally report theoretical results on randomized generation of primitive sets of matrices: a set of permutation matrices with a 0 entry changed into a 1 is primitive and has exponent of O(n log n) with high probability in case of uniform random distribution and the same holds for a random set of binary matrices where each entry is set, independently, equal to 1 with probability p and equal to 0 with probability 1-p , when np-log n - > infty as n - > infty .

BibTeX - Entry

@InProceedings{catalano_et_al:LIPIcs:2018:9630,
  author =	{Costanza Catalano and Rapha{\"e}l M. Jungers},
  title =	{{On Randomized Generation of Slowly Synchronizing Automata}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9630},
  URN =		{urn:nbn:de:0030-drops-96305},
  doi =		{10.4230/LIPIcs.MFCS.2018.48},
  annote =	{Keywords: Synchronizing automata, random automata, Cern{\'y} conjecture, automata with simple idempotents, primitive sets of matrices}
}

Keywords: Synchronizing automata, random automata, Cerný conjecture, automata with simple idempotents, primitive sets of matrices
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018

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