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Tradeoffs for language recognition on parallel computing models

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Automata, Languages and Programming (ICALP 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 226))

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Abstract

The alternating machine having a separate input tape with k two-way, read-only heads, and a certain number of internal configurations — AM(k) is considered as a parallel computing model. For the complexity measure TIME·SPACE·PARALLELISM (TSP), the optimal lower bounds ω(n2) and ω (n3/2) resp. are proved for the recognition of specific languages on AM (1), and AM(k) respectively. For the complexity measure REVERSALS·SPACE·PARALLELISM (RSP), the lower bound ω(n1/3/log2n) is established for the recognition of a specific language on AM(k). This result implies a polynomial lower bound on PTIME·HARDWARE of parallel RAM's. All lower bounds obtained are substantially improved for the case that SPACE ≥nɛ, for 0 < ɛ < 1. Several strongest lower bounds for two-way (and one-way) alternating (deterministic, and nondeterministic) multihead finite automata are obtained as direct consequences of these results.

This work was supported in part by the grant SPZV I-1-5/8.

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Authors and Affiliations

  1. Dept. of Theoretical Cybernetics and Mathematical Informatics, Comenius University, 842 15, Bratislava, Czechoslovakia

    Juraj Hromkovič

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  1. Juraj Hromkovič
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Laurent Kott

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© 1986 Springer-Verlag Berlin Heidelberg

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Hromkovič, J. (1986). Tradeoffs for language recognition on parallel computing models. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_65

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  • DOI: https://doi.org/10.1007/3-540-16761-7_65

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  • Print ISBN: 978-3-540-16761-7

  • Online ISBN: 978-3-540-39859-2

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