2 research outputs found
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg,
1966). Since that time, a vast literature on computational and descriptional
complexity issues on multi-head finite automata documenting the importance of
these devices has been developed. Although multi-head finite automata are a
simple concept, their computational behavior can be already very complex and
leads to undecidable or even non-semi-decidable problems on these devices such
as, for example, emptiness, finiteness, universality, equivalence, etc. These
strong negative results trigger the study of subclasses and alternative
characterizations of multi-head finite automata for a better understanding of
the nature of non-recursive trade-offs and, thus, the borderline between
decidable and undecidable problems. In the present paper, we tour a fragment of
this literature
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