相关论文: On the subset sum problem over finite fields
A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably)…
The hitting set problem asks for a collection of sets over a universe $U$ to find a minimum subset of $U$ that intersects each of the given sets. It is NP-hard and equivalent to the problem set cover. We give a branch-and-bound algorithm to…
We generalize the classical knapsack and subset sum problems to arbitrary groups and study the computational complexity of these new problems. We show that these problems, as well as the bounded submonoid membership problem, are P-time…
In this paper, we consider a problem of counting multiplicities. We fix a counting function of multiplicity of rational points in a hypersurface of a projective space over a finite field, and we give an upper bound for the sum with respect…
Approximating Subset Sum is a classic and fundamental problem in computer science and mathematical optimization. The state-of-the-art approximation scheme for Subset Sum computes a $(1-\varepsilon)$-approximation in time…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
We discuss a structural approach to subset-sum problems in additive combinatorics. The core of this approach are Freiman-type structural theorems, many of which will be presented through the paper. These results have applications in various…
We show that Reed-Solomon codes of dimension $k$ and block length $n$ over any finite field $\mathbb{F}$ can be deterministically list decoded from agreement $\sqrt{(k-1)n}$ in time $\text{poly}(n, \log |\mathbb{F}|)$. Prior to this work,…
We study product sets of finite arithmetic progressions of polynomials over a finite field. We prove a lower bound for the size of the product set, uniform in a wide range of parameters. We apply our results to resolve the function field…
This paper describes several new problems and ideas concerning algebraic geometry and complexity theory. It first uses the idea of coloring graphs with elements of finite fields. This procedure then shows that graph coloring problems can be…
The main computational steps in algebraic soft-decoding, as well as Sudan-type list-decoding, of Reed-Solomon codes are bivariate polynomial interpolation and factorization. We introduce a computational technique, based upon re-encoding and…
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
This paper deals with a universal coding problem for a certain kind of multiterminal source coding network called a generalized complementary delivery network. In this network, messages from multiple correlated sources are jointly encoded,…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
We describe a simple analytical method for effective summation of series, including divergent series. The method is based on self-similar approximation theory resulting in self-similar root approximants. The method is shown to be general…
MDS codes and self-dual codes are important families of classical codes in coding theory. It is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field $F_q$ is completely solved for $q$ is…
Subspace codes were introduced in order to correct errors and erasures for randomized network coding, in the case where network topology is unknown (the noncoherent case). Subspace codes are indeed collections of subspaces of a certain…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
In this paper, we survey the complexity of distinct methods that allow the programmer to synthesize a sup-interpretation, a function providing an upper- bound on the size of the output values computed by a program. It consists in a static…
Delsarte's method and its extensions allow to consider the upper bound problem for codes in 2-point-homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that…