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- W1975320892 abstract "For the first time we separate the widely used shared-memory models of parallel computation, COMMON( m ), ARBITRARY( m ), and PRIORITY( m ), for small m (the communication width), without the restrictive assumption that each processor has access only to one input . Rather we follow S. A. Cook and C. Dwork (1982 , in “Proceedings, 14th ACM Symp. on Theory of Computing, 1982”, pp. 231–233) and U. Vishkin and A. Wigderson (1985 , SIAM J. Comput. 14 , No. 2, 303–314) who assume that the inputs are given in a read only memory (ROM). The previous separation results of F. Fich, P. Ragde, and A. Wigderson (1984 , in “Proceedings, 3rd ACM Symp. on Principles of Distrib. Comput., 1984,” pp. 179–184) and F. Fich, F. Meyer, P. Ragde, and A. Wigderson (1985 , in “Proceedings, 17th ACM Symp. on Theory of Comput., 1985,” pp. 48–58) (Familiarity with these papers would be helpful.) do assume that each processor knows only one input. We introduce a new technique to separate (COMMON( m ) with ROM and ARBITRARY(1) (even without ROM). We also generalize a technique of (Fich, Ragde, and Wigderson, op cit. ) to separate ARBITRARY( m ) with ROM and PRIORITY(1) (even without ROM). These two separation results are tight. Fich, Ragde, and Wigderson ( ibid. ) have previously obtained tight separation results for the corresponding models without ROM. Also we settle a conjecture of Vishkin and Wigderson about the parallel time (depth) needed to compute PARITY nondeterministically on a PRIORITY(1). They conjecture that the lower bound is Ω(√n) which is the same as the deterministic tight lower bound. We prove a nondeterministic upper bound of O(n 1 3 ) . We also prove a tight lower bound of Ω(√n) for PARITY on nondeterministic PRIORITY(1) without ROM and a lower bound of Ω( log log n) for PARITY on nondeterministic PRIORITY(1) with ROM." @default.
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- W1975320892 date "1987-05-01" @default.
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- W1975320892 title "Separation and lower bounds for ROM and nondeterministic models of parallel computation" @default.
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- W1975320892 doi "https://doi.org/10.1016/0890-5401(87)90017-4" @default.
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