A Note on Nondeterminism in Small, Fast Parallel Computers

Nondeterministic analogues of the well-known classes NC and SC, d d NNC and NSC, respectively, are investigated. Adding nondeterminism to SC leaves it in the domain of parallel computation since NSC E POLYLOGSPACE. That is, NSC is a subset of the class of languages computable by fast parallel computers. Adding noodeterminism to NC appears to make it much more powerful since NNC = NP. It is clear that NSCE NNC, and probable that NSC C NNC. We provide further evidence for this conjeeture by showing that NSC is precisely the class of languages recognizable in simultaneous polynomial time and polylog reversals by a nondeterministic Turing machine with a read-only input tape and a single read-write work-tape. It is known that NNC is precisely the class of languages recognizable in simultaneous polynomial time and polylog reversals by a nondeterministic Turing machine with a read-only input tape and two read-write work-tapes. Index Terns-Crossing sequence, NC, nondeterminism, parallel computation thesis, parallel computers, reversal, SC, simultaneous resource bounds, space, time.