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Complexity of Closeness, Sparseness and Segment Equivalence for Context-Free and Regular Languages

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Informatik

Part of the book series: TEUBNER-TEXTE zur Informatik ((TTZI,volume 1))

Abstract

In this paper, we investigate the complexity of deciding closeness, segment equivalence and sparseness for context-free and regular languages. It will be shown that the closeness problem for context-free grammars (CFGs) is undecidable while it is PSPACE-complete for nondeterministic finite automata (NFAs) and NL-complete for deterministic finite automata (DFAs). The segment equivalence problems for CFGs and NFAs are co-NP-complete. It is NL-complete for DFAs. If encoded in binary, the segment equivalence problems for CFGs and NFAs are co-NE-complete and PSPACE-complete, respectively. The sparseness problems for NFAs and DFAs are NL-complete. We also show that the equivalence problems for CFGs and NFAs generating commutative languages are II P 2 -complete and co-NP-complete, respectively. For trim DFAs generating commutative languages the equivalence problem is in L.

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Author information

Authors and Affiliations

  1. Computer Science Program, University of Texas at Dallas, Richardson, Texas, 75083, USA

    Dung T. Huynh

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  1. Dung T. Huynh
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Editor information

Editors and Affiliations

  1. Universität Saarbrücken, Deutschland

    Johannes Buchmann , Harald Ganzinger  & Wolfgang J. Paul ,  & 

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© 1992 B. G. Teubner Verlagsgesellschaft, Leipzig

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Huynh, D.T. (1992). Complexity of Closeness, Sparseness and Segment Equivalence for Context-Free and Regular Languages. In: Buchmann, J., Ganzinger, H., Paul, W.J. (eds) Informatik. TEUBNER-TEXTE zur Informatik, vol 1. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-95233-2_14

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  • DOI: https://doi.org/10.1007/978-3-322-95233-2_14

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-8154-2033-1

  • Online ISBN: 978-3-322-95233-2

  • eBook Packages: Springer Book Archive

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