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Parallel complexity of logical query programs

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Abstract

We consider the parallel time complexity of logic programs without function symbols, called logical query programs, or Datalog programs. We give a PRAM algorithm for computing the minimum model of a logical query program, and show that for programs with the “polynomial fringe property,” this algorithm runs in time that is logarithmic in the input size, assuming that concurrent writes are allowed if they are consistent. As a result, the “linear” and “piecewise linear” classes of logic programs are inN C. Then we examine several nonlinear classes in which the program has a single recursive rule that is an “elementary chain.” We show that certain nonlinear programs are related to GSM mappings of a balanced parentheses language, and that this relationship implies the “polynomial fringe property;” hence such programs are inN C Finally, we describe an approach for demonstrating that certain logical query programs are log space complete forP, and apply it to both elementary single rule programs and nonelementary programs.

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Author notes

  1. Allen Van Gelder

    Present address: Department of Computer Science, University of California, 95064, Santa Cruz, CA, USA

Authors and Affiliations

  1. Department of Computer Science, Stanford University, 94305, Stanford, CA, USA

    Jeffrey D. Ullman & Allen Van Gelder

Authors
  1. Jeffrey D. Ullman
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  2. Allen Van Gelder
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Additional information

Communicated by Jeffrey Scott Vitter.

Supported by NSF Grant IST-84-12791, a grant of IBM Corporation, and ONR contract N00014-85-C-0731.

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Ullman, J.D., Van Gelder, A. Parallel complexity of logical query programs. Algorithmica 3, 5–42 (1988). https://doi.org/10.1007/BF01762108

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