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.2019.127
URN: urn:nbn:de:0030-drops-107037
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10703/
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Raszyk, Martin ; Basin, David ; Traytel, Dmitriy

From Nondeterministic to Multi-Head Deterministic Finite-State Transducers

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LIPIcs-ICALP-2019-127.pdf (0.5 MB)

Abstract

Every nondeterministic finite-state automaton is equivalent to a deterministic finite-state automaton. This result does not extend to finite-state transducers - finite-state automata equipped with a one-way output tape. There is a strict hierarchy of functions accepted by one-way deterministic finite-state transducers (1DFTs), one-way nondeterministic finite-state transducers (1NFTs), and two-way nondeterministic finite-state transducers (2NFTs), whereas the two-way deterministic finite-state transducers (2DFTs) accept the same family of functions as their nondeterministic counterparts (2NFTs).
We define multi-head one-way deterministic finite-state transducers (mh-1DFTs) as a natural extension of 1DFTs. These transducers have multiple one-way reading heads that move asynchronously over the input word. Our main result is that mh-1DFTs can deterministically express any function defined by a one-way nondeterministic finite-state transducer. Of independent interest, we formulate the all-suffix regular matching problem, which is the problem of deciding for each suffix of an input word whether it belongs to a regular language. As part of our proof, we show that an mh-1DFT can solve all-suffix regular matching, which has applications, e.g., in runtime verification.

BibTeX - Entry

@InProceedings{raszyk_et_al:LIPIcs:2019:10703,
  author =	{Martin Raszyk and David Basin and Dmitriy Traytel},
  title =	{{From Nondeterministic to Multi-Head Deterministic Finite-State Transducers}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{127:1--127:14},
  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/2019/10703},
  URN =		{urn:nbn:de:0030-drops-107037},
  doi =		{10.4230/LIPIcs.ICALP.2019.127},
  annote =	{Keywords: Formal languages, Nondeterminism, Multi-head automata, Finite transducers}
}

Keywords: Formal languages, Nondeterminism, Multi-head automata, Finite transducers
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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