相关论文: Lower Bounds for the Size of Nondeterministic Circ…

In 1978 Sakoda and Sipser raised the question of the cost, in terms of size of representations, of the transformation of two-way and one-way nondeterministic automata into equivalent two-way deterministic automata. Despite all the attempts,…

We establish a connection between linear complementary dual (LCD) codes and caps in projective space. Using this framework and the structure theory of maximal caps, we derive nonexistence theorems for LCD codes with minimum distance at…

Reversible circuits have been studied extensively and intensively, and have plenty of applications in various areas, such as digital signal processing, cryptography, and especially quantum computing. In 2003, the lower bound $\Omega(2^n…

Neural gates compute functions based on weighted sums of the input variables. The expressive power of neural gates (number of distinct functions it can compute) depends on the weight sizes and, in general, large weights (exponential in the…

We investigate monotone circuits with local oracles [K., 2016], i.e., circuits containing additional inputs $y_i = y_i(\vec{x})$ that can perform unstructured computations on the input string $\vec{x}$. Let $\mu \in [0,1]$ be the locality…

This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…

The performance of low-density parity-check (LDPC) codes at high signal-to-noise ratios (SNRs) is known to be limited by the presence of certain sub-graphs that exist in the Tanner graph representation of the code, for example trapping sets…

Noisy computation and reversible computation have been studied separately, and it is known that they are as powerful as unrestricted computation. We study the case where both noise and reversibility are combined and show that the combined…

Nonuniform families of polynomial-size finite automata, which are series of indexed finite automata having polynomially many inner states, are used in the past literature to solve nonuniform families of promise decision problems. Among such…

In the 2017 paper by Dougherty, Kim, Ozkaya, Sok, and Sol\'e about the linear programming bound for LCD codes the notion $\mathrm{LCD}[n,k]$ was defined for binary LCD $[n,k]$-codes. We find the formula for $\mathrm{LCD}[n,2]$.

In this paper, we study the nonrelativistic limit of normalized solutions for the following nonlinear Dirac equation (NLDE) on noncompact metric graph $\G$ with finitely many edges and a non-empty compact core $\K$ \begin{equation*} \D u -…

This paper focuses on finite-dimensional upper and lower bounds on decodable thresholds of Zm and binary low-density parity-check (LDPC) codes, assuming belief propagation decoding on memoryless channels. A concrete framework is presented,…

We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the…

We prove a tight lower bound (up to constant factors) on the sample complexity of any non-interactive local differentially private protocol for optimizing a linear function over the simplex. This lower bound also implies a tight lower bound…

Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In…

We consider the problem of computing a binary linear transformation using unreliable components when all circuit components are unreliable. Two noise models of unreliable components are considered: probabilistic errors and permanent errors.…

We demonstrate a family of propositional formulas in conjunctive normal form so that a formula of size $N$ requires size $2^{\Omega(\sqrt[7]{N/logN})}$ to refute using the tree-like OBDD refutation system of Atserias, Kolaitis and Vardi…

We study the limit of D-series minimal models when the central charge tends to a generic irrational value $c\in (-\infty, 1)$. We find that the limit theory's diagonal three-point structure constant differs from that of Liouville theory by…

We present a formulation of the problem of finding the smallest T -Count circuit that implements a given unitary as a binary search over a sequence of continuous minimization problems, and demonstrate that these problems are numerically…

The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…