The problem of space invariance for sequential machines

  • Authors:

  • Cees Slot;Peter van Emde Boas

  • Affiliations:

  • Department of Mathematics and Computer Science, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands;Department of Mathematics and Computer Science, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands

  • Venue:
  • Information and Computation
  • Year:
  • 1988

Quantified Score

Hi-index 0.00

Visualization

Abstract

In complexity theory the use of informal estimates can be justified by appealing to the Invariance Thesis which states that all standard models of sequential computing devices are equivalent in the sense that the fundamental complexity classes do not depend on the precise model chosen for their definition. This thesis would require, among others, that a RAM can be simulated by a Turing machine with constant factor overhead in space. We argue that the definition of RAM space, at least in the manner it is traditionally given in the literature, is inadequate for this purpose. The invariance thesis can be validated only in a weak interpretation. The rather complicated simulation which achieves the constant factor space overhead is based on a new method for condensing space and uses perfect hash functions with minimal program size.