Related papers: Solving promise equations over monoids and groups
Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
A class of smoothing methods is proposed for solving mathematical programs with equimibrium constraints. We introduce new and very simple regularizations of the complementarity constraints. Some estimate distance to optimal solution and…
We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
The conformal crossing equation puts very stringent constraints on the conformal data. We formulate it in way that makes the conformal symmetry more transparent. This allows for generalization of the crossing equation to arbitrary Lie group…
We present an algorithmic approach to the conjugacy problems in monoids and semigroups, using rewriting systems. There is a class of monoids and semigroups that satisfy the condition that the transposi- tion problem and the left and right…
We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach that combines numerical algebraic geometry and sums of squares…
This survey aims at demonstrating that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed many problems can be NP-hard when considering general precedence constraints, while they…
In an additive factorial monoid each element can be represented as a linear combination of irreducible elements (atoms) with uniquely determined coefficients running over all natural numbers. In this paper we develop for a wide class of…
We present the MEoP problem that decides the existence of solutions to certain modular equations over prime numbers and show how this separates the complexity class NP from its subclass P
A polynomial complexity algorithm is designed which tests whether a point belongs to a given tropical linear variety.
We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub, and Smale for…
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…
The polynomial hierarchy has been widely studied in classical complexity theory. In this paper, we will generalize some commonly known results about the polynomial hierarchy to a version of the hierarchy extended to promise problems. This…
In order to get $\lambda$-models with a rich structure of $\infty$-groupoid, which we call "homotopy $\lambda$-models", a general technique is described for solving domain equations on any cartesian closed $\infty$-category (c.c.i.) with…