Time bounded random access machines

  • Authors:
  • Stephen A. Cook;Robert A. Reckhow

  • Affiliations:
  • -;-

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 1973

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Abstract

The RAM, an abstract model for a random access computer, is introduced. A unique feature of the model is that the execution time of an instruction is defined in terms of l(n), a function of the size of the numbers manipulated by the instruction. This model has a fixed program, but it is shown that the computing speeds of this model and a stored-program model can differ by no more than a constant factor. It is proved that a T(n) time-bounded Turing machine can be simulated by an O(T(n).l(T(n))) timebounded RAM, and that a T(n) time-bounded RAM can be simulated by a Turing machine whose execution time is bounded by (T(n))^3 if l(n) is constant, or (T(n))^2 if l(n) is logarithmic. The main result states that if T"2(n) is a function such that there is a RAM that computes T"2(n) in time O(T"2(n)), and if T"1(n) is any function such that liminfn-~T"1(n)T"2(n)=0, then there is a set S that can be recognized by some RAM in time O(T"2(n)), but no RAM recognizes S in time O(T"1(n)). This is a sharper diagonal result than has been obtained for Turing machines. The proofs of most of the above results are constructive and are aided by the introduction of an ALGOL-like programming language for RMA's.