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URN: urn:nbn:de:0030-drops-13194
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Complexity of solutions of equations over sets of natural numbers

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Abstract

Systems of equations over sets of natural numbers (or, equivalently, language equations over a one-letter alphabet) of the form $X_i=varphi_i(X_1, ldots, X_n)$ ($1 leqslant i leqslant n$) are considered. Expressions $varphi_i$ may contain the operations of union, intersection and pairwise sum $A plus B = {x + y mid x in A, y in B$. A system with an EXPTIME-complete least solution is constructed, and it is established that least solutions of all such systems are in EXPTIME. The general membership problem for these equations is proved to be EXPTIME-complete.

BibTeX - Entry

@InProceedings{okhotin_et_al:LIPIcs:2008:1319,
  author =	{Alexander Okhotin and Artur Jez},
  title =	{{Complexity of solutions of equations  over sets of natural numbers}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{373--384},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Susanne Albers and Pascal Weil},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1319},
  URN =		{urn:nbn:de:0030-drops-13194},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2008.1319},
  annote =	{Keywords: }
}

Seminar: 25th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2008
Date of publication: 2008


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