Related papers: A Separation of NP and coNP in Multiparty Communic…

For any $\{0,1\}$-valued function $f$, its \emph{$n$-folded XOR} is the function $f^{\oplus n}$ where $f^{\oplus n}(X_1, \ldots, X_n) = f(X_1) \oplus \cdots \oplus f(X_n)$. Given a procedure for computing the function $f$, one can apply a…

The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we look at the link between the P - NP question and the "Deterministic" versus "Non Deterministic"…

Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of…

Our main result is a succinct counterpoint to Courcelle's meta-theorem as follows: every cw-nontrivial monadic second-order (MSO) property is either NP-hard or coNP-hard over graphs given by succinct representations. Succint representations…

This paper gives a nearly tight characterization of the quantum communication complexity of the permutation-invariant Boolean functions. With such a characterization, we show that the quantum and randomized communication complexity of the…

This paper establishes the separation of complexity classes $\mathbf{P}$ and $\mathbf{NP}$ through a novel homological algebraic approach grounded in category theory. We construct the computational category $\mathbf{Comp}$, embedding…

This paper studies the complexity of solving two classes of non-cooperative games in a distributed manner in which the players communicate with a set of system nodes over noisy communication channels. The complexity of solving each game…

We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…

A subset of the integer planar grid $[N] \times [N]$ is called corner-free if it contains no triple of the form $(x,y), (x+\delta,y), (x,y+\delta)$. It is known that such a set has a vanishingly small density, but how large this density can…

Buhrman, Cleve and Wigderson (STOC'98) observed that for every Boolean function $f : \{-1, 1\}^n \to \{-1, 1\}$ and $\bullet : \{-1, 1\}^2 \to \{-1, 1\}$ the two-party bounded-error quantum communication complexity of $(f \circ \bullet)$ is…

We study M(n), the number of distinct values taken by multinomial coefficients with upper entry n, and some closely related sequences. We show that both pP(n)/M(n) and M(n)/p(n) tend to zero as n goes to infinity, where pP(n) is the number…

In quantum information, nonlocal games are particularly useful for differentiating classical, quantum, and non-signalling correlations. An example of differentiation is given by the principle of no-collapse of communication complexity,…

A new class UF of problems is introduced, strictly included in the class NP, which arises in the analysis of the time verifying the intermediate results of computations. The implications of the introduction of this class are considered.…

Adleman, DeMarrais, and Huang introduced the nondeterministic quantum polynomial-time complexity class NQP as an analogue of NP. Fortnow and Rogers implicitly showed that, when the amplitudes are rational numbers, NQP is contained in the…

We present a quasipolynomial-time algorithm for solving the weak membership problem for the convex set of separable, i.e. non-entangled, bipartite density matrices. The algorithm decides whether a density matrix is separable or whether it…

The P versus NP problem is studied under the relational model of E. F. Codd. I found that the term "complete configuration" is unnecessary and harmful in computational complexity theory because of excessive symbol redundancy. For an input,…

Recently, Brassard et. al. conjectured that the fact that the maximal possible correlations between two non-local parties are the quantum-mechanical ones is linked to a reasonable restriction on communication complexity. We provide further…

We develop an extension of the process matrix (PM) framework for correlations between quantum operations with no causal order that allows multiple rounds of information exchange for each party compatibly with the assumption of well-defined…

We prove new bounds on the quantum communication complexity of the disjointness and equality problems. For the case of exact and non-deterministic protocols we show that these complexities are all equal to n+1, the previous best lower bound…

Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two polynomials in F_p[X] of degree less than n. For n large compared to p, we establish the bound M_p(n) = O(n log n 8^(log^* n) log p), where log^* is the iterated…