The complexity of the inequivalence problem for regular expressions with intersection

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Abstract

The nondeterministic lower space bound √n of Hunt, for the problem if a regular expression with intersection describes a non-empty language, is improved to the upper bound n. For the general inequivalence problem for regular expressions with intersection the lower bound cn matches the upper bound except for the constant c. And the proof for this tight lower bound is simpler than the proofs for previous bounds. Methods developed in a result about one letter alphabets are extended to get a complete characterization for the problem of deciding if one input-expression describes a given language. The complexity depends only on the property of the given language to be finite, infinite but bounded, or unbounded.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 7th Colloquium
EditorsJaco de Bakker, Jan van Leeuwen
PublisherSpringer Verlag
Pages234-245
Number of pages12
ISBN (Print)9783540100034
DOIs
Publication statusPublished - Jan 1 1980
Event7th International Colloquium on Automata, Languages and Programming, ICALP 1980 - Noordwijkerhout, Netherlands
Duration: Jul 14 1980Jul 18 1980

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume85 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Colloquium on Automata, Languages and Programming, ICALP 1980
CountryNetherlands
CityNoordwijkerhout
Period7/14/807/18/80

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Furer, M. (1980). The complexity of the inequivalence problem for regular expressions with intersection. In J. de Bakker, & J. van Leeuwen (Eds.), Automata, Languages and Programming - 7th Colloquium (pp. 234-245). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 85 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-10003-2_74