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1997 Technical Reports

Parallel RAMs with Owned Global Memory

Patrick W. Dymond and Walter L. Ruzzo

Technical Report CS-97-02

York University

February 1997


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 realizing a full CREW-PRAM model, it is interesting to observe that in fact, most known CREW-PRAM algorithms satisfy the CROW restriction or can be easily modified to do so.

This paper makes three main contributions. First, we formally define the CROW-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 $O(\log n)$ 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 in time order of (n to the power1+ epsilon) over S(n) for any epsilon > 0 and any S(n) satisfying square of log n < =S(n) <=n on a deterministic auxiliary pushdown automaton having a log n space work tape, pushdown store of maximum height S(n), and random access to its input tape. These results extend and unify work of von Braunmuhl, Cook, Mehlhorn, and Verbeek; Klein and Reif; and Rytter.

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