Parallelism in random access machines

@article{Fortune1978ParallelismIR,
  title={Parallelism in random access machines},
  author={Steven Fortune and Jim Wyllie},
  journal={Proceedings of the tenth annual ACM symposium on Theory of computing},
  year={1978}
}
  • S. Fortune, J. Wyllie
  • Published 1 May 1978
  • Computer Science
  • Proceedings of the tenth annual ACM symposium on Theory of computing
A model of computation based on random access machines operating in parallel and sharing a common memory is presented. [] Key Result Similar results hold for other classes. The effect of limiting the size of the common memory is also considered.
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It is shown that parallelism uniformly speeds up time bounded Probabilistic sequential RAM computations by nearly a quadratic factor, and that probabilistic choice can be, eliminated from parallel computation by introducing nonuniformity.
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This paper introduces a formal model for random access computers and argues that the model is a good one to use in the theory of computational complexity and shows the existence of a time complexity hierarchy which is finer than any standard abstract computer model.
On the Power of Multiplication in Random Access Machines
TLDR
It is proved that, counting one operation as a unit of time and considering the machines as acceptors, deterministic and nondeterministic polynomial time acceptable languages are the same, and are exactly the languages recognizable in polynomially tape by Turing machines.
Time Bounded Random Access Machines with Parallel Processing
The RAM model of Cook and Reckhow ~s extended to allow parallel recursive calls and the elementary theory of such machines is developed The uniform cost criterion is used The results include proofs
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It is shown that NP is equal to the class of sets accepted by this model in nondeterministic time 0(log n), and this result is generalized to arbitrary time classes.
A characterization of the power of vector machines
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Random access machines (RAMs) are usually defined to have registers that hold integers, but their ability to operate bit by bit on the bit vectors used to represent integers is overlooked, so a vector machine is called.
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TLDR
A natural characterization of the polynomial time hierarchy of Stockmeyer and Meyer in terms of parallel machines is given, and a generalization of Saviten's result NONDET-L(n)-SPACE ⊆ L(n)2-SPACE is given.
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It will be shown in the sequel that the parallel arithmetic complexity of all these four problems is upper bounded by O(log2n) and the algorithms that establish this bound use a number of processors polynomial in n, disproves I. Munro's conjecture.
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Parallel Solution of Recurrence Problems
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It is shown that if the recurrence function f has associated with it two other functions that satisfy certain composition properties, then it can be constructed elegant and efficient parallel algorithms that can compute all N elements of the series in time proportional to ⌈log2N⌉.
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