Abstract

The importance of reversal complexity as a basic computational resource has only been recognized in recent years. It is intimately connected to parallel time complexity and circuit depth. In this paper, some basic techniques necessary for establishing analogues of well-known theorems on space and time complexity are developed. The main results are, for reversal-constructible functions $s(n) \geqq \log n$, \[ \textit{DSPACE} (s(n)) \subseteq \textit{DREVERSAL}(s(n)), \] and a tape reduction theorem. As applications of the tape reduction theorem, a hierarchy theorem is proved and the existence of complete languages for reversal complexity is shown.

MSC codes

  1. 68Q05
  2. 68Q10
  3. 68Q15

Keywords

  1. reversal
  2. space
  3. tape reduction theorem
  4. reversal hierarchies
  5. complete languages
  6. parallel complexity

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Information

Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 622 - 638
ISSN (online): 1095-7111

History

Submitted: 30 June 1986
Accepted: 11 October 1990
Published online: 13 July 2006

MSC codes

  1. 68Q05
  2. 68Q10
  3. 68Q15

Keywords

  1. reversal
  2. space
  3. tape reduction theorem
  4. reversal hierarchies
  5. complete languages
  6. parallel complexity

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