相关论文: One-Dimensional Peg Solitaire

For every fixed class of regular languages, there is a natural hierarchy of increasingly more general problems: Firstly, the membership problem asks whether a given language belongs to the fixed class of languages. Secondly, the separation…

One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a…

I present a single algorithm which solves the clique problems, "What is the largest size clique?", "What are all the maximal cliques?" and the decision problem, "Does a clique of size k exist?" for any given graph in polynomial time. The…

Matching Logic is a framework for specifying programming language semantics and reasoning about programs. Its formulas are called patterns and are built with variables, symbols, connectives and quantifiers. A pattern is a combination of…

We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…

In this paper, we consider the rank-one tensor completion problem. We address the question of existence and uniqueness of the rank-one solution. In particular we show that the global uniqueness over the field of real numbers can be verified…

For generic maps from compact surfaces with boundary into the plane we develop an explicit algorithm for minimizing both the number of cusps and the number of components of the singular locus. More precisely, we minimize among maps with…

It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a…

The regular separability problem asks, for two given languages, if there exists a regular language including one of them but disjoint from the other. Our main result is decidability, and PSpace-completeness, of the regular separability…

We prove lower bounds on the length of regular expressions for finite languages by methods from arithmetic circuit complexity. First, we show a reduction: the length of a regular expression for a language $L\subseteq \{0,1\}^n$ is bounded…

This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…

We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…

This work aims to study and explore the use of Gene Expression Programming (GEP) in solving the on-line Bin-Packing problem. The main idea is to show how GEP can automatically find acceptable heuristic rules to solve the problem efficiently…

We consider the problem of assigning radii to a given set of points in the plane, such that the resulting set of circles is connected, and the sum of radii is minimized. We show that the problem is polynomially solvable if a connectivity…

Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…

The Clique Problem has a reduction to the Maximum Flow Network Interdiction Problem. We review the reduction to evolve a polynomial time algorithm for the Clique Problem. A computer program in C language has been written to validate the…

We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…

Given a language, which in this article is a set of strings of some fixed length, we study the problem of producing its elements by a procedure in which each position has its own local rule. We introduce a way of measuring how much…

In this paper we give a new aggregation framework for linear Diophantine equations. In particular, we prove that an aggregated system of minimum size can be built in polynomial time. We also derive an analytic formula that gives the number…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…