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.ICALP.2019.105
URN: urn:nbn:de:0030-drops-106814
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10681/
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Bell, Paul C.

Polynomially Ambiguous Probabilistic Automata on Restricted Languages

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LIPIcs-ICALP-2019-105.pdf (0.5 MB)

Abstract

We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for non-strict cut-points of polynomially ambiguous PFA remains undecidable even when the input word is over a bounded language and all PFA transition matrices are commutative. In doing so, we introduce a new technique based upon the Turakainen construction of a PFA from a Weighted Finite Automata which can be used to generate PFA of lower dimensions and of subexponential ambiguity. We also study freeness/injectivity problems for polynomially ambiguous PFA and study the border of decidability and tractability for various cases.

BibTeX - Entry

@InProceedings{bell:LIPIcs:2019:10681,
  author =	{Paul C. Bell},
  title =	{{Polynomially Ambiguous Probabilistic Automata on Restricted Languages}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{105:1--105:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10681},
  URN =		{urn:nbn:de:0030-drops-106814},
  doi =		{10.4230/LIPIcs.ICALP.2019.105},
  annote =	{Keywords: Probabilistic finite automata, ambiguity, undecidability, bounded language, emptiness}
}

Keywords: Probabilistic finite automata, ambiguity, undecidability, bounded language, emptiness
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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