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 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...
We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard...
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...
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-...