License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ICALP.2018.123
URN: urn:nbn:de:0030-drops-91270
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Descotte, MarĂ­a Emilia ; Figueira, Diego ; Puppis, Gabriele

Resynchronizing Classes of Word Relations

LIPIcs-ICALP-2018-123.pdf (0.7 MB)


A natural approach to define binary word relations over a finite alphabet A is through two-tape finite state automata that recognize regular languages over {1, 2} x A, where (i,a) is interpreted as reading letter a from tape i. Accordingly, a word w in L denotes the pair (u_1,u_2) in A^* x A^* in which u_i is the projection of w onto i-labelled letters. While this formalism defines the well-studied class of Rational relations (a.k.a. non-deterministic finite state transducers), enforcing restrictions on the reading regime from the tapes, which we call synchronization, yields various sub-classes of relations. Such synchronization restrictions are imposed through regular properties on the projection of the language onto {1,2}. In this way, for each regular language C subseteq {1,2}^*, one obtains a class Rel({C}) of relations. Regular, Recognizable, and length-preserving rational relations are all examples of classes that can be defined in this way.
We study the problem of containment for synchronized classes of relations: given C,D subseteq {1,2}^*, is Rel({C}) subseteq Rel({D})? We show a characterization in terms of C and D which gives a decidability procedure to test for class inclusion. This also yields a procedure to re-synchronize languages from {1, 2} x A preserving the denoted relation whenever the inclusion holds.

BibTeX - Entry

  author =	{Mar{\'i}a Emilia Descotte and Diego Figueira and Gabriele Puppis},
  title =	{{Resynchronizing Classes of Word Relations}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{123:1--123:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-91270},
  doi =		{10.4230/LIPIcs.ICALP.2018.123},
  annote =	{Keywords: synchronized word relations, containment, resynchronization}

Keywords: synchronized word relations, containment, resynchronization
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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