Parallelism in random access machines

TLDR

The computational power of the parallel random access machine model relates to that of traditional computational models. The paper presents a parallel random access machine model that operates on shared memory. The model uses parallel random access machines with shared memory, and the study also examines the impact of limiting the memory size. Deterministic parallel RAMs accept exactly the polynomial‑time languages of polynomial‑tape bounded Turing machines, while nondeterministic parallel RAMs accept exactly the languages of nondeterministic exponential‑time bounded Turing machines, with analogous results for other complexity classes.

Abstract

A model of computation based on random access machines operating in parallel and sharing a common memory is presented. The computational power of this model is related to that of traditional models. In particular, deterministic parallel RAM's can accept in polynomial time exactly the sets accepted by polynomial tape bounded Turing machines; nondeterministic RAM's can accept in polynomial time exactly the sets accepted by nondeterministic exponential time bounded Turing machines. Similar results hold for other classes. The effect of limiting the size of the common memory is also considered.