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.2019.22
URN: urn:nbn:de:0030-drops-102614
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10261/
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Descotte, María Emilia ; Figueira, Diego ; Figueira, Santiago

Closure Properties of Synchronized Relations

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LIPIcs-STACS-2019-22.pdf (0.5 MB)

Abstract

A standard approach to define k-ary word relations over a finite alphabet A is through k-tape finite state automata that recognize regular languages L over {1, ..., k} x A, where (i,a) is interpreted as reading letter a from tape i. Accordingly, a word w in L denotes the tuple (u_1, ..., u_k) in (A^*)^k in which u_i is the projection of w onto i-labelled letters. While this formalism defines the well-studied class of rational relations, 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 L onto {1, ..., k}. In this way, for each regular language C subseteq {1, ..., k}^*, one obtains a class Rel({C}) of relations. Synchronous, Recognizable, and Length-preserving rational relations are all examples of classes that can be defined in this way.
We study basic properties of these classes of relations, in terms of closure under intersection, complement, concatenation, Kleene star and projection. We characterize the classes with each closure property. For the binary case (k=2) this yields effective procedures.

BibTeX - Entry

@InProceedings{descotte_et_al:LIPIcs:2019:10261,
  author =	{Mar{\'i}a Emilia Descotte and Diego Figueira and Santiago Figueira},
  title =	{{Closure Properties of Synchronized Relations}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Rolf Niedermeier and Christophe Paul},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10261},
  doi =		{10.4230/LIPIcs.STACS.2019.22},
  annote =	{Keywords: synchronized word relations, rational, closure, characterization, intersection, complement, Kleene star, concatenation}
}

Keywords: synchronized word relations, rational, closure, characterization, intersection, complement, Kleene star, concatenation
Collection: 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)
Issue Date: 2019
Date of publication: 12.03.2019

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