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URN: urn:nbn:de:0030-drops-74089
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Word Equations in Nondeterministic Linear Space

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Abstract

Satisfiability of word equations is an important problem in the intersection of formal languages and algebra: Given two sequences consisting of letters and variables we are to decide whether there is a substitution for the variables that turns this equation into true equality of strings. The computational complexity of this problem remains unknown, with the best lower and upper bounds being, respectively, NP and PSPACE. Recently, the novel technique of recompression was applied to this problem, simplifying the known proofs and lowering the space complexity to (nondeterministic) O(n log n). In this paper we show that satisfiability of word equations is in nondeterministic linear space, thus the language of satisfiable word equations is context-sensitive. We use the known recompression-based algorithm and additionally employ Huffman coding for letters. The proof, however, uses analysis of how the fragments of the equation depend on each other as well as a new strategy for nondeterministic choices of the algorithm, which uses several new ideas to limit the space occupied by the letters.

BibTeX - Entry

@InProceedings{jez:LIPIcs:2017:7408,
  author =	{Artur Jez},
  title =	{{Word Equations in Nondeterministic Linear Space}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{95:1--95:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7408},
  URN =		{urn:nbn:de:0030-drops-74089},
  doi =		{10.4230/LIPIcs.ICALP.2017.95},
  annote =	{Keywords: Word equations, string unification, context-sensitive languages, space efficient computations, linear space}
}

Keywords: Word equations, string unification, context-sensitive languages, space efficient computations, linear space
Seminar: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue date: 2017
Date of publication: 2017


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