This paper studies quantum Arthur–Merlin games, which are Arthur–Merlin games in which Arthur and Merlin can perform quantum computations and Merlin can send Arthur quantum in...
We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolm...
This paper develops new relationships between resource-bounded dimension, entropy rates, and compression. New tools for calculating dimensions are given and used to improve previo...
We study several properties of sets that are complete for NP. We prove that if L is an NP-complete set and S ⊇ L is a p-selective sparse set, then L − S is ≤p m-hard for NP....
This paper investigates the powers and limitations of quantum entanglement in the context of cooperative games of incomplete information. We give several examples of such nonlocal...
An NP search problem is the problems of finding a witness to the given NP predicate, and TFNP is the class of total NP search problems. TFNP contains a number of subclasses conta...
We study the robustness of complete sets for various complexity classes. A complete set A is robust if for any f(n)-dense set S ∈ P, A−S is still complete, where f(n) ranges f...
The language compression problem asks for succinct descriptions of the strings in a language A such that the strings can be efficiently recovered from their description when given...
We consider the problem of testing bipartiteness in the adjacency matrix model. The best known algorithm, due to Alon and Krivelevich, distinguishes between bipartite graphs and g...
Entanglement is an essential resource for quantum communication and quantum computation, similar to shared random bits in the classical world. Entanglement distillation extracts n...