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ATIME(n) is closed under Counting

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Mathematical Foundations of Computer Science 1990 (MFCS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 452))

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Abstract

It has been recently found out that different variations of counting play an important role in structural complexity theory (for example, it has been argued that the ability of counting is closely related with the ability of nondeterministic complementation). In this paper it is proved that ATIME(T(n)) classes, for T(n)≥n, are closed under counting. Thus exponentially many words, each of size O(n), can be counted by an alternating Turing machine in the optimal time O(n).

This research was supported by the grant RP.I.09 from the Institute of Informatics, University of Warsaw.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Przesmyckiego 20, 51-151, Wrocław, Poland

    Marek Piotrów

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  1. Marek Piotrów
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Branislav Rovan

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© 1990 Springer-Verlag Berlin Heidelberg

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Piotrów, M. (1990). ATIME(n) is closed under Counting. In: Rovan, B. (eds) Mathematical Foundations of Computer Science 1990. MFCS 1990. Lecture Notes in Computer Science, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029642

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  • DOI: https://doi.org/10.1007/BFb0029642

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52953-8

  • Online ISBN: 978-3-540-47185-1

  • eBook Packages: Springer Book Archive

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