Tradeoffs for language recognition on alternating machines

AbstractThe alternating machine having a separate input tape with k two-way, read-only heads, and a certain number of internal configurations, AM(k), is considered as a parallel computing model. For the complexity measure TIME · SPACE · PARALLELISM (TSP), the optimal lower bounds Ω(n2) and Ω(n3/2) respectively are proved for the recognition of specific languages on AM(1) and AM(k) respectively. For the complexity measure REVERSALS · SPACE · PARALLELISM (RSP), the lower bound Ω(n1/2) is established for the recognition of a specific language on AM(k). This result implies a polynomial lower bound on PARALLEL TIME · HARDWARE of parallel RAM's.Lower bounds on the complexity measures TIME · SPACE and REVERSALS · SPACE of nondeterministic machines are direct consequences of the result introduced above.All lower bounds obtained are substantially improved in the case that SPACE⩾ nɛ for 0<ɛ<1. Several strongest lower bounds for two-way and one-way alternating (deterministic, nondeterministic) multihead finite automata are obtained as direct consequences of these results. The hierarchies for the complexity measures TSP, RSP, TS and RS can be immediately achieved too

Deterministic versus nondeterministic space in terms of synchronized alternating machines

AbstractThe study of synchronized alternating machines has enabled to characterize several natural complexity classes. It is known that synchronized alternating space SASPACE(S(n))= ∪c>0NSPACE(ncS(n)) for any (space-constructible) function S(n) [Hromkovicˇet al. (1991)]. In particular, context-sensitive languages are characterized by two-way synchronized alternating finite automata. Furthermore, PSPACE is characterized by synchronized alternating multihead finite automata and NLOG by synchronized alternating two-way finite automata with parallelism bounded by a constant. In the present paper we prove analogous characterizations for deterministic space classes using a restricted form of synchronization — globally deterministic synchronization. This enables to study the well-known open problems concerning nondeterminism versus determinism as problems about synchronization. We also show that globally deterministic synchronization is strictly more powerful than deterministic synchronization