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

Abstract

We identify and study a frequently occurring subclass of Concurrent-Read, Exclusive-Write Parallel Random Access Machines (CREW-PRAM's). Called Concurrent-Read, Owner -Write, or CROW-PRAM's, 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. Most known CREW-PRAM algorithms are in fact CROW-PRAM algorithms. We show that the class of languages recognizable in time O(logn) on CROW-PRAM's is precisely equal to the class LOGDCFL of languages log space reducible to deterministic context free languages, and demonstrate the stability of the CROW-PRAM model. Our characterization theorem is based on a new and simpler proof of a result due to Klein and Reif that the recognition problem for any deterministic context free language can be solved in time O(logn) on a CREW-PRAM. We show that the simulation can actually be carried out on the CROW-PRAM model mentioned above. Next, using the same basic machinery, we give a new and simpler proof of the results by von Braunmühl, Cook, Mehlhorn, and Verbeek that DCFL recognition can be done in O(log2n) space and polynomial time, simultaneously, i.e. in SC2. Further, we obtain a technical improvement to their result in that our algorithm requires only a O(log2n) height pushdown store, rather than general space.