We continue the investigation of interactive proofs with bounded
communication, as initiated by Goldreich and Hastad (IPL 1998).
Let $L$ be a language that has an interactive proof in which the prover
sends few (say $b$) bits to the verifier.
We prove that the complement $\bar L$ has ... more >>>

Local receptive field neurons comprise such well-known and widely
used unit types as radial basis function neurons and neurons with
center-surround receptive field. We study the Vapnik-Chervonenkis
(VC) dimension of feedforward neural networks with one hidden layer
of these units. For several variants of local receptive field
neurons we show ... more >>>

We consider some problems about pairs of disjoint $NP$ sets.
The theory of these sets with a natural concept of reducibility
is, on the one hand, closely related to the theory of proof
systems for propositional calculus, and, on the other, it
resembles the theory of NP completeness. Furthermore, such
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