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.CSL.2018.14
URN: urn:nbn:de:0030-drops-96815
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9681/
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Chadha, Rohit ; Sistla, A. Prasad ; Viswanathan, Mahesh

Approximating Probabilistic Automata by Regular Languages

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LIPIcs-CSL-2018-14.pdf (0.6 MB)

Abstract

A probabilistic finite automaton (PFA) A is said to be regular-approximable with respect to (x,y), if there is a regular language that contains all words accepted by A with probability at least x+y, but does not contain any word accepted with probability at most x. We show that the problem of determining if a PFA A is regular-approximable with respect to (x,y) is not recursively enumerable. We then show that many tractable sub-classes of PFAs identified in the literature - hierarchical PFAs, polynomially ambiguous PFAs, and eventually weakly ergodic PFAs - are regular-approximable with respect to all (x,y). Establishing the regular-approximability of a PFA has the nice consequence that its value can be effectively approximated, and the emptiness problem can be decided under the assumption of isolation.

BibTeX - Entry

@InProceedings{chadha_et_al:LIPIcs:2018:9681,
  author =	{Rohit Chadha and A. Prasad Sistla and Mahesh Viswanathan},
  title =	{{Approximating Probabilistic Automata by Regular Languages}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic  (CSL 2018)},
  pages =	{14:1--14:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Dan Ghica and Achim Jung},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9681},
  URN =		{urn:nbn:de:0030-drops-96815},
  doi =		{10.4230/LIPIcs.CSL.2018.14},
  annote =	{Keywords: Probabilistic Finite Automata, Regular Languages, Ambiguity}
}

Keywords: Probabilistic Finite Automata, Regular Languages, Ambiguity
Collection: 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)
Issue Date: 2018
Date of publication: 29.08.2018

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