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International Meeting of Young Computer Scientists

IMYCS 1990: Aspects and Prospects of Theoretical Computer Science pp 148–158Cite as

Characterizing complexity classes by higher type

Primitive recursive definitions, part II

  • Part III Communications
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 464))

Abstract

Higher type primitive recursive definitions (also known as Gödel's system T) defining first-order functions (i.e. functions of type ind→...→ind→ind, ind for individuals, higher types occur in between) can be classified into an infinite syntactic hierarchy: A definition is in the n'th stage of this hierarchy, a so called rank-n-definition, iff n is an upper bound on the levels of the types occurring in it.

We interpret these definitions over finite structures and show for n≥1: Rank-(2n+2)-definitions characterize (in the sense of [Gu83], say) the complexity class DTIME(expn(poly)) whereas rank-(2n+3)-definitions characterize DSPACE(expn(poly)) (here exp0(x) = x, expn+1(x)=2exp n x). This extends the results that rank-1-definitions characterize LOGSPACE [Gu83], rank-2-definitions characterize PTIME, rank-3-definitions characterize PSPACE, rank-4-definitions characterize EXPTIME [Go89a].

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik Fachgebiet Praktische Informatik, Universität -GH- Duisburg, Lotharstrasse 65, D-4100, Duisburg 1, West-Germany

    Andreas Goerdt

  2. Fachbereich Informatik, Universität des Saarlandes, Im Stadtwald, D-6600, Saarbrücken 11, West-Germany

    Helmut Seidl

Authors
  1. Andreas Goerdt
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  2. Helmut Seidl
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Editor information

Jürgen Dassow Jozef Kelemen

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© 1990 Springer-Verlag Berlin Heidelberg

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Goerdt, A., Seidl, H. (1990). Characterizing complexity classes by higher type. In: Dassow, J., Kelemen, J. (eds) Aspects and Prospects of Theoretical Computer Science. IMYCS 1990. Lecture Notes in Computer Science, vol 464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53414-8_37

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  • DOI: https://doi.org/10.1007/3-540-53414-8_37

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53414-3

  • Online ISBN: 978-3-540-46869-1

  • eBook Packages: Springer Book Archive

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