It is shown that the PL hierarchy PLH = PL S PL PL S PL PL PL S \Delta \Delta \Delta, defined in terms of the Ruzzo-Simon-Tompa relativization, collapses to PL. Also, it is shown that PL is closed under logspace-uniform AC 0 -reductions. 1 Introduction The power of probabilistic

prove th:rt. in spite of their analogy with the polynomial time hierarchy, the finite lev-rls of this hierarchy collapse t,o Afsf=Ah42). Using a com-binatorial lemma on finite groups [IIE], we construct a game by whirh t.he nondeterministic player (Merlin) is able to coavlnre the random player (Arthur

with several alternations of fixed point and negation. This proves that the fixed point query hierarchy suggested by Chandra and Harel collapses at the first fixed point level. It is also a general result showing that in finite model theory one application of fixed point suffices. Introduction and Summary

viewdependent simplification. Briefly, HDS works by clustering vertices together in a hierarchical fashion. The simplification process continuously queries this hierarchy to generate a scene containing only those polygons that are important from the current viewpoint. When the volume of space associated with a

on the collapse of the log space hierarchies [10, 2, 14]. We have shown that the class (FO + pos TC) is closed under complementation. Our

with access to satisfiability. We show that every language with a bounded round Arthur-Merlin game has subexponential size membership proofs for infinitely many input lengths unless exponential time coincides with the third level of the polynomial-time hierarchy (and hence the polynomial-time hierarchy

We discuss the advantage of using hierarchy in testing. Our demonstration is based on the problem of fault collapsing. Though this problem is not considered to be too complex, the time of collapsing faults in moderately large circuits can be several hours or more. This can be considerably shortened

We show that every constraint satisfaction problem over a fixed constraint language that has bounded relational width has also relational width (2, 3). Together with known results this gives a trichotomy for width: a constraint satisfaction problem has either relational width 1, or relational width (2, 3) (and no smaller width), or does not have bounded relational width.

nondeterministic function, then the polynomial hierarchy collapses to its second level. As the existence of such a function is known to be equivalent to the statement "every multivalued NP function has a single-valued NP refinement," our result provides the strongest evidence yet that multivalued NP

this paper we show that the log space oracle hierarchy also collapses, that it thus does coincide with the log space alternation hierarchy, and that the resulting complexity class L has other interesting characterizations in terms of circuits with oracle gates