. We consider uniform subclasses of the nonuniform complexity classes defined by Karp and Lipton [23] via the notion of advice functions. These subclasses are obtained by restricting the complexity of computing correct advice. We also investigate the effect of allowing advice functions of limited complexity to depend on the input rather than on the input's length. Among other results, using the notions described above, we give new characterizations of (a) NP NP"SPARSE , (b) NP with a restricted access to an NP oracle and (c) the odd levels of the boolean hierarchy. As a consequence, we show that every set that is nondeterministically truth-table reducible to SAT in the sense of Rich [35] is already deterministically truth-table reducible to SAT. Furthermore, it turns out that the NP reduction classes of bounded versions of this reducibility coincide with the odd levels of the boolean hierarchy. Key words. nonuniform complexity classes, advice classes, optimization functions, restric...

In this paper, we give several generalized theorems concerning reducibility notions to certain complexity classes. We study classes that are either (I) closed under NP many-one reductions and polynomial time conjunctive reductions or (II) closed under coNP many-one reductions and polynomial time disjunctive reductions. We prove that for such a class K, reducibility notions of sets to K under polynomial time constant-round truth-table reducibility, polynomial time log-Turing reducibility, logspace constant-round truth-table reducibility, logspace log-Turing reducibility and logspace Turing reducibility are all equivalent and (2) every set that is polynomial time positive Turing reducible to a set in K is already in K. From these results, we derive some observations on the reducibility notions to C=P and NP.

In this paper, we study the computational power of an SIMD type parallel computation model with simple processors, called cube-APA. Some relationships between the computational power of cube-APAs that run with at most k alternations in communication and the polynomial time hierarchy are stated. 1 Introduction Research on complexity theory has proved that many problems in various fields are NP - complete or NP-hard. One of demands for parallel computation is to give practical solutions for such intractable problems. It is very important to study theoretically relationships between the computational power of a parallel computation model and its functions to explain essential power of parallelism. From this point of view, SIMD (Single Instruction stream Multiple Data stream) type parallel computation models with simple processors, such as FRAM (Random Access Machine with a Functional Memory) [6] and processor array type models, have been studied. In this paper, we also study the computat...

this paper to study the expressive power of bounded existential quantification in polynomial-time computability. Our goal was to characterize nondeterministic polynomial-time computations in a machine-independent way. The following considerations are intended to make our idea clear. Let # be the finite alphabet