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A hierarchy of probabilistic complexity classes generalizing NP has recently emerged in the work of [Ba], [GMR], and [GS]. The IP hierarchy is defined through the notion of an interactive proof system, in which an all powerful prover tries to convince a probabilistic polynomial time verifier that a string w is in a language L. The verifier tosses coins and exchanges messages back and forth with the...
An interactive proof system with Perfect Completeness (resp. Perfect Soundness) for a language L is an interactive proof (for L) in which for every x ∈ L (resp. x ∉ L) the verifier always accepts (resp. always rejects). Zachos and Fuerer showed that any language having a bounded interactive proof has one with perfect completeness. We extend their result and show that any language having a (possibly...
The Boolean Decision tree model is perhaps the simplest model that computes Boolean functions; it charges only for reading an input variable. We study the power of randomness (vs. both determinism and non-determinism) in this model, and prove separation results between the three complexity measures. These results are obtained via general and efficient methods for computing upper and lower bounds on...
Expanding graphs are the basic building blocks used in constructions of graphs with special connectivity properties such as superconcentrators. The only known explicit method (Margulis[7], Gabber and Galil[5]) of constructing arbitrarily large expanding graphs with a linear number of edges, uses graphs whose edges are defined by a finite set of linear mappings restricted to a two-dimensional set,...
Decision procedures for validity in intuitionistic propositional calculus and modal propositional calculus are given which require a running time proportional to a polynomial in the length of the formula on a nondeterministic Turing machine. Using a theorem of Cook's and well-known transformations from intuitionistic to classical and modal to intuitionistic logics, the validity problem for intuitionistic...
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