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Polynomial size test sets for context-free languages

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Automata, Languages and Programming (ICALP 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 623))

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Abstract

We prove that each context-free language has a polynomial size test set. This improves the doubly exponential upper bound obtained in [ACK] and single exponential bound from [KRJ]. An efficient algorithm to find test sets for contextfree languages is also presented. The basic tools in the proof are graph-theoretical properties of test sets and periodicities in strings.

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Bibliography

  1. Albert,J.,CulikII,K. and Karhumaki J., Test sets for context free languages and algebraic systems of equations, Inform. Control 52 (1982) 172–186.

    Article  Google Scholar 

  2. Albert,M.H. and Lawrence J., A proof of Ehrenfeucht conjecture, Theoret. Comp. Science 41 (1985) 121–123

    Article  Google Scholar 

  3. Culik II,K., Homomorphisms: Decidability, Equality and Test Sets, in R. Book (ed.), Formal Language Theory, Perspectives and Open Problems (Academic Press, 1980).

    Google Scholar 

  4. Culik II,K. and Salomaa,A., On the decidability of homomorphism equivalence for languages. J. Comput. System Sci. 17 (1978)163–175.

    Article  Google Scholar 

  5. Culik II, K. and Salomaa,A., Test sets and checking words for homomorphism equivalence, J. Comput. System Sci. 20 (1980) 375–395.

    Article  Google Scholar 

  6. Hopcroft J., Ullman J., Introduction to the theory of automata, languages and computation, Addison Wesley (1979)

    Google Scholar 

  7. Karhumaki,J., The Ehrenfeucht conjecture: a compactness claim for finitely generated free monoids, Theoret.Comp.Science 29 (1984) 285–308

    Article  Google Scholar 

  8. KarhumakiJ., On recent trends in formal language theory, Lect. Notes in Comp. Science 267 (1987) 136–162

    Google Scholar 

  9. Karhumaki J., Rytter W. and Jarominek S., Efficient construction of test sets for regular and context free languages, MFCS'91, Lect.Notes in Comp.Science (1991)

    Google Scholar 

  10. Lothaire, Combinatorics on words, Academic Press (1985)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Turku University, Finland

    Juhani Karhumaäki

  2. Institute of Informatics, Department of Mathematics and Informatics, Warsaw University, ul. Banacha 2, 00-913, Warszawa, Poland

    Wojciech Plandowski & Wojciech Rytter

Authors
  1. Juhani Karhumaäki
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  2. Wojciech Plandowski
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  3. Wojciech Rytter
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Editor information

W. Kuich

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© 1992 Springer-Verlag Berlin Heidelberg

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Karhumaäki, J., Plandowski, W., Rytter, W. (1992). Polynomial size test sets for context-free languages. In: Kuich, W. (eds) Automata, Languages and Programming. ICALP 1992. Lecture Notes in Computer Science, vol 623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55719-9_63

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  • DOI: https://doi.org/10.1007/3-540-55719-9_63

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55719-7

  • Online ISBN: 978-3-540-47278-0

  • eBook Packages: Springer Book Archive

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