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- W3099041864 abstract "Why should we believe that NC does not equal P? One form of evidence is that many people have tried, but failed, to show them equal. More persuasive, perhaps, is the way they have failed, or rather, the character of the limited successes. Specifically, known approaches consistently leave a large gap between what we know how to solve by highly parallel algorithms, and general problems in P. In outline, the state of the art is as follows. General simulations are not fast: The best known parallel simulations of general sequential models give very modest improvements, basically reducing sequential time T to parallel time T/logT or √T, depending on the parallel model. Furthermore, 2TΩ(1) processors are needed to achieve even these modest improvements. Fast simulations are not general: Rapid simulations of sequential models by highly parallel models are known only for rather weak sequential models. Natural approaches provably fail: Certain natural approaches to highly parallel simulation are provably insufficient. Equivalently, in certain natural structured models of computation (Borodin [41]), one can prove that the analogs of NC and P are not equal, and indeed are separated by a nearly exponential gap, as suggested by the two points above. In this chapter we will present this evidence in more detail. The nature of the available evidence renders this chapter, especially Section 5.4, somewhat more technical than the rest of Part I. The reader may wish to skim or skip it, at least on first reading. First, consider the Generic Machine Simulation Problem introduced in Section 4.1. Intuitively, why should we expect this problem to be hard to parallelize? Notice that we defined the problem in terms of Turing machines as a technical convenience; they are not in any way fundamental to the result." @default.
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- W3099041864 date "1995-06-01" @default.
- W3099041864 modified "2023-09-27" @default.
- W3099041864 title "Evidence That NC Does Not Equal P" @default.
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