Related papers: Notes on the Polish Algorithm
We develop tools for analyzing focused stochastic local search algorithms. These are algorithms which search a state space probabilistically by repeatedly selecting a constraint that is violated in the current state and moving to a random…
We consider algebras with one binary operation $\cdot$ and one generator ({\it monogenic}) and satisfying the left distributive law $a\cdot (b\cdot c)=(a\cdot b)\cdot (a\cdot c)$. One can define a sequence of finite left-distributive…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
We discuss the allocation of finite resources in the presence of a logarithmic diminishing return law, in analogy to some results from Information Theory. To exemplify the problem we assume that the proposed logarithmic law is applied to…
The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…
A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…
Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown frequently and well before convergence has been achieved. These algorithms are typically based on recurrence relations which involve formal orthogonal…
We study Polynomial Lawvere logic PL, a logic defined over the Lawvere quantale of extended positive reals with sum as tensor, to which we add multiplication, thereby obtaining a semiring structure. PL is designed for complex quantitative…
Coalgebra is a currently quite active field, which aims to look at generic state-based systems (most prominently automata) from a very abstract point of view, mainly using tools from category theory. One of its achievements is to give a…
We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…
We begin the systematic study of decision problems for finitely generated groups given by a solution to their word problem. We relate this to the study of computable analysis on the space of marked groups. We point out that several distinct…
Distribution matchers for finite alphabets are shown to have informational divergences that grow logarithmically with the block length, generalizing a basic result for binary strings.
The standard two-sided and one-sided matching problems, and the closely related school choice problem, have been widely studied from an axiomatic viewpoint. A small number of algorithms dominate the literature. For two-sided matching, the…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This note discusses how to find an optimized randomization scheme for this algorithm, which is related…
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…