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.STACS.2016.34
URN: urn:nbn:de:0030-drops-57355
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5735/
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Fijalkow, Nathanaël

Characterisation of an Algebraic Algorithm for Probabilistic Automata

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Abstract

We consider the value 1 problem for probabilistic automata over finite words: it asks whether a given probabilistic automaton accepts words with probability arbitrarily close to 1. This problem is known to be undecidable. However, different algorithms have been proposed to partially solve it; it has been recently shown that the Markov Monoid algorithm, based on algebra, is the most correct algorithm so far. The first contribution of this paper is to give a characterisation of the Markov Monoid algorithm.

The second contribution is to develop a profinite theory for probabilistic automata, called the prostochastic theory. This new framework gives a topological account of the value 1 problem, which in this context is cast as an emptiness problem. The above characterisation is reformulated using the prostochastic theory, allowing to give a modular proof.

BibTeX - Entry

@InProceedings{fijalkow:LIPIcs:2016:5735,
  author =	{Nathana{\"e}l Fijalkow},
  title =	{{Characterisation of an Algebraic Algorithm for Probabilistic Automata}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{34:1--34:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5735},
  URN =		{urn:nbn:de:0030-drops-57355},
  doi =		{10.4230/LIPIcs.STACS.2016.34},
  annote =	{Keywords: Probabilistic Automata, Value 1 Problem, Markov Monoid Algorithm, Algebraic Algorithm, Profinite Theory, Topology in Computer Science}
}

Keywords: Probabilistic Automata, Value 1 Problem, Markov Monoid Algorithm, Algebraic Algorithm, Profinite Theory, Topology in Computer Science
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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