相关论文: Lower bounds for some decision problems over C

In this note, we provide a wide range of upper bounds for the moduli of the zeros of a complex polynomial. The obtained bounds complete a series of previous papers on the location of zeros of polynomials.

We present new upper bounds on the parameters of batch codes with restricted query size. These bounds are an improvement on the Singleton bound. The techniques for derivations of these bounds are based on the ideas in the literature for…

In this paper, we consider classes of decision tables closed under removal of attributes (columns) and changing of decisions attached to rows. For decision tables from closed classes, we study lower bounds on the minimum cardinality of…

An explicit upper bound is established for the least non-trivial integer zero of an arbitrary cubic form $C \in \mathbb{Z}[X_1,...,X_n],$ provided that $n \geq 14.$

We provide bounds on the size of operators obtained by algorithms for executing D-finite closure properties. For operators of small order, we give bounds on the degree and on the height (bit-size). For higher order operators, we give degree…

We obtained some upper bounds for the pseudocharacter of the space C(X,Y) at a point f.

Programs to solve so-called constraint problems are complex pieces of software which require many design decisions to be made more or less arbitrarily by the implementer. These decisions affect the performance of the finished solver…

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…

We propose a method for computing upper bounds for the Heilbronn problem for triangles.

We study the computational complexity of decision problems in $k$-level linear programming (LP). Seminal work by Jeroslow establishes that determining whether the optimal objective value of a $k$-level LP is at least as good as a given…

In this note, we extend the result of \cite{PoulyG16} about the complexity of solving polynomial differential equations over unbounded domains to work with non-rational input. In order to deal with arbitrary input, we phrase the result in…

In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool…

We present an algorithm for computing upper bounds for the Online Bin Stretching Problem with a small number of bins and the resulting upper bounds for 4, 5 and 6 bins. This both demonstrates the possibility of using computer search for…

We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this…

New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine…

Polynomial solving algorithms are essential to applied mathematics and the sciences. As such, reduction of their complexity has become an incredibly important field of topological research. We present a topological approach to constructing…

We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is…

We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.

We compute the Hilbert coefficients of a graded module with pure resolution and discuss lower and upper bounds for these coefficients for arbitrary graded modules.