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Quantum entanglement is a fundamental property of quantum mechanics and it serves as a basic resource in quantum computation and information. Despite its importance, the power and limitations of quantum entanglement are far from being fully ...

We investigate autoreducibility properties of complete sets for NEXP under different polynomial-time reductions. Specifically, we show under some polynomial-time reductions that there are complete sets for NEXP that are not autoreducible. We obtain the ...

An input-oblivious proof system is a proof system in which the proof does not depend on the claim being proved. Input-oblivious versions of NP and MA were introduced in passing by Fortnow, Santhanam, and Williams, who also showed that those classes are ...

The class ACC consists of circuit families with constant depth over unbounded fan-in AND, OR, NOT, and MOD_m gates, where m > 1 is an arbitrary constant. We prove the following.

---NEXP, the class of languages accepted in nondeterministic exponential time,...

A typical problem in database theory is to verify whether there exists a relation (or database) instance satisfying a number of given dependency constraints. This problem has recently received a renewed deal of interest within the context of data ...

We investigate the question whether NE can be separated from the reduction closures of tally sets, sparse sets and NP. We show that (1) $\mathrm{NE}\not\subseteq R^{\mathrm{NP}}_{n^{o(1)}-T}(\mathrm{TALLY})$ ; (2) $\mathrm{NE}\not\subseteq R^{SN}_{m}(\mathrm{SPARSE})$ ; (3) $\mathrm{NEXP}\not\subseteq \mathrm{P}^{\mathrm{NP}}_{n^{k}-T}/n^{k}$ for all k 1; and (4) $\mathrm{NE}\not\subseteq \mathrm{P}_{btt}(\mathrm{NP}\oplus\mathrm{SPARSE})$ . Result (3) extends a previous result by Mocas to nonuniform reductions. We also ...

The class ACC consists of circuit families with constant depth over unbounded fan-in AND, OR, NOT, and MOD$m$ gates, where $m > 1$ is an arbitrary constant. We prove:- $NTIME[2^n]$ does not have non-uniform ACC circuits of polynomial size. The size ...

We continue an investigation into resource-bounded Kolmogorov complexity (Allender et al., 2006 [4]), which highlights the close connections between circuit complexity and Levin's time-bounded Kolmogorov complexity measure Kt (and other measures with a ...

Variants of Kannan’s Theorem are given where the circuits of the original theorem are replaced by arbitrary recursively presentable classes of languages that use advice strings and satisfy certain mild conditions. Let poly_k denote those functions ...

We show that derandomizing Polynomial Identity Testing is, essentially, equivalent to proving circuit lower bounds for NEXP. More precisely, we prove that if one can test in polynomial time (or, even, nondeterministic subexponential time, infinitely ...

Game-theoretic characterisations of complexity classes have often proved useful in understanding the power and limitations of these classes. One well-known example tells us that PSPACE can be characterized by two-person, perfect-information games in ...

We show that every m-complete set for NEXP as well as its complement have an infinite subset in P. This answers an open question first raised by L. Berman (1976).