Parallel RAMs with owned global memory and deterministic context-free language recognition

  • Authors:
  • Patrick W. Dymond;Walter L. Ruzzo

  • Affiliations:
  • York Univ., Toronto, Ont., Canada;Univ. of Washington, Seattle

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 2000

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Abstract

We identify and study a natural and frequently occurring subclass of Concurrent Read, Exclusive Write Parallel Random Access Machines (CREW-PRAMs). Called Concurrent Read, Owner Write, or CROW-PRAMS, these are machines in which each global memory location is assigned a unique “owner” processor, which is the only processor allowed to write into it. Considering the difficulties that would be involved in physically realizinga full CREW-PRAM model and demonstrate its stability under several definitional changes. Second, we precisely characterize the power of the CROW-PRAM by showing that the class of languages recognizable by it in time O(log n) (and implicity with a polynomial number of processors) is exactly the class LOGDCFL of languages log space reducible to deterministic context-free languages. Third, using the same basic machinery, we show that the recognition problem for deterministic context-free languages can be solved quickly on a deterministic auxilliary pushdown automation having random access to its input tape, a log n space work tape, and pushdown store of small maximum height. For example, time O(n1 + &egr;) is achievable with pushdown height O(log2 n). These result extend and unify work of von Braunmöhl, Cook, Mehlhorn, and Verbeek, Klein and Reif; and Rytter.