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We present a new, combinatorial proof of the classical theorem that the analytic sets are not closed under complement. Possible connections with questions in complexity theory are discussed.
Let EH be the hypothesis that a certain type of expander graph has an explicit construction. Let io-SPACE(T(n)) be the class of problems solvable by algorithms which for infinitely many inputs use at most space t(n). Then the following holds: There exists ε>0 such that for any time bound t(n), $$EH \to (P = R or (TIME(t(n)) \cap \{ 1\} * ) \subseteq io - SPACE(t^{1 - \varepsilon } (n))$$...
We study on-line strategies for solving problems with hybrid algorithms. There is a problemQandw basicalgorithms for solvingQ. For some λ≤w, we have a computer with λ disjoint memory areas, each of which can be used to run a basic algorithm and store its intermediate results. In the worst case, only one basic algorithm can solveQin finite time, and all of the other basic algorithms run forever without...
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...
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