Motivated by recent work on quantum black-box query complexity, we consider quantum versions of two wellstudied models of learning Boolean functions: Angluin’s model of exact le...
We use hypotheses of structural complexity theory to separate various NP-completeness notions. In particular, we introduce an hypothesis from which we describe a set in NP that is...
We study the complexity of approximating the VC dimension of a collection of sets, when the sets are encoded succinctly by a small circuit. We show that this problem is • Σp 3-...
Restricting the search space {0, 1}n to the set of truth tables of “easy” Boolean functions on log n variables, as well as using some known hardness-randomness tradeoffs, we ...
Russell Impagliazzo, Valentine Kabanets, Avi Wigde...
We give a simple analysis of the PCP with low amortized query complexity of Samorodnitsky and Trevisan [16]. The analysis also applies to the linearity testing over finite field...
This paper explores the difference between parallel and serial queries to an NP-complete oracle, SAT, from the perspective of functions with a limited number of output bits. For ...
The quantum version of communication complexity allows the two communicating parties to exchange qubits and/or to make use of prior entanglement (shared EPRpairs). Some lower boun...