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Mathematical systems theory

, Volume 3, Issue 2, pp 125–129 | Cite as

Two memory bounds for the recognition of primes by automata

  • J. Hartmanis
  • H. Shank
Article

Abstract

This paper establishes two bounds for the rate of growth of memory in automata which recognize the set of primes.

Keywords

Computational Mathematic Memory Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    M. Minsky andS. Papert, Unrecognizable sets of numbers.J. Assoc. Comput. Machinery 13 (1966), 281–286.Google Scholar
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    M. P. Schützenberger, A remark on acceptable sets of numbers.J. Assoc. Comput. Machinery 15 (1968), 300–303.Google Scholar
  3. [3]
    J. Hartmanis andH. Shank, On the recognition of primes by automata.J. Assoc. Comput. Machinery 15 (1968), 382–389.Google Scholar
  4. [4]
    A. E. Ingham, On the difference between consecutive primes.Quarterly J. of Math. (Oxford Series)8 (1937), 255–266.Google Scholar
  5. [5]
    D. Allen, Jr., On a characterization of the nonregular set of primes.J. Comp. System Science 1 (1968), 464–467.Google Scholar

Copyright information

© Swets & Zeitlinger B.V. 1969

Authors and Affiliations

  • J. Hartmanis
    • 1
  • H. Shank
    • 1
  1. 1.Department of Computer ScienceCornell UniversityUSA

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