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Chomsky hierarchy and communication complexity

  • Chapter 1 Languages
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Machines, Languages, and Complexity (IMYCS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 381))

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Abstract

Chomsky hierarchy is compared with the hierarchy of communication complexity for VLSI. It is shown that only regular languages belong to the same levels of both hierarchies. There are hard languages according to Chomsky hierarchy that belong to the lowest level in communication complexity hierarchy. On the other hand there is a deterministic linear language that requires the highest (linear) communication complexity. This is the main result because it implies that VLSI circuits need Θ(n) area and Θ(n2) area. (time)2 complexity to recognize deterministic context-free languages which solves an open problem of Hromkovič [7].

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Ždanovova 6, 040 01, Košice, Czechoslovakia

    Galina Jirásková

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  1. Galina Jirásková
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J. Dassow J. Kelemen

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© 1989 Springer-Verlag Berlin Heidelberg

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Jirásková, G. (1989). Chomsky hierarchy and communication complexity. In: Dassow, J., Kelemen, J. (eds) Machines, Languages, and Complexity. IMYCS 1988. Lecture Notes in Computer Science, vol 381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015924

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  • DOI: https://doi.org/10.1007/BFb0015924

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51516-6

  • Online ISBN: 978-3-540-48203-1

  • eBook Packages: Springer Book Archive

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