A note on nondeterminism in small, fast parallel computers

Nondeterministic analogues of the well-known language classes NC and SC called NNC and NSC, respectively, are investigated. NC is the class of languages that can be accepted by small, fast parallel computers; SC is the class of languages that can be recognized by a deterministic Turing machine in polynomial time and polylog tape-head reversals. Adding nondeterminism to SC leaves it in the domain of parallel computation since NSC⊆POLYLOGSPACE. That is, NSC is a subset of the class of languages computable by fast parallel computers. Adding nondeterminism to NC appears to make it much more powerful since NNC=NP. It is clear that NSC⊆NNC, and probable that NSC⊂NNC. Further evidence for this conjecture is provided 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 similar, but is recognizable by a Turing machine with two read-write tapes