Parallel computation with threshold functions

Preliminary version
  • Ian Parberry
  • Georg Schnitger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 223)


We study two classes of unbounded fan-in parallel computation, the standard one, based on unbounded fan-in ANDs and ORs, and a new class based on unbounded fan-in threshold functions. The latter is motivated by a connectionist model of the brain used in Artificial Intelligence. We are interested in the resources of time and address complexity. Intuitively, the address complexity of a parallel machine is the number of bits needed to describe an individual piece of hardware. We demonstrate that (for WRAMs and uniform unbounded fan-in circuits) parallel time and address complexity is simultaneously equivalent to alternations and time on an alternating Turing machine (the former to within a constant multiple, and the latter a polynomial). In particular, for constant parallel time, the latter equivalence holds to within a constant multiple. Thus, for example, polynomial-processor, constant-time WRAMs recognize exactly the languages in the logarithmic time hierarchy, and polynomial-word-size, constant-time WRAMs recognize exactly the languages in the polynomial time hierarchy. As a corollary, we provide improved simulations of deterministic Turing machines by constant-time shared-memory machines. Furthermore, in the threshold model, the same results hold if we replace the alternating Turing machine with the analogous threshold Turing machine, and replace the resource of alternations with the corresponding resource of thresholds. Threshold parallel computers are much more powerful than the standard models (for example, with only polynomially many processors, they can compute the parity function and sort in constant time, and multiply two integers in O(log*n) time), and appear less amenable to known lower-bound proof techniques.


Parallel Computation Parallel Machine Turing Machine Threshold Function Constant Multiple 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Ian Parberry
    • 1
  • Georg Schnitger
    • 1
  1. 1.Department of Computer ScienceThe Pennsylvania State UniversityUniversity Park

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