Related papers: A Context for Paris-Harrington Combinatorial Princ…
Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which -- under standard assumptions in complexity theory -- cannot be solved in…
We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point purely in terms of the original Hamiltonian, avoiding the normalization procedure.…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
The mathematical notion of incompleteness (eg of rational numbers, Turing-computable functions, and arithmetic proof) does not play a key role in conventional physics. Here, a reformulation of the kinematics of quantum theory is attempted,…
In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with H\"{o}lder continuous coefficients. This is of course out of reach by using…
Substitutability, interchangeability and related concepts in Constraint Programming were introduced approximately twenty years ago and have given rise to considerable subsequent research. We survey this work, classify, and relate the…
Twenty years ago, in an article titled "Covariance and contravariance: conflict without a cause", I argued that covariant and contravariant specialization of method parameters in object-oriented programming had different purposes and…
In various application fields, such as fluid-, cell-, or crowd-simulations, spatial data structures are very important. They answer nearest neighbor queries which are instrumental in performing necessary computations for, e.g., taking the…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of this process we propose a principle that generalizations of mathematical structures that are…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
A formalisation of G\"odel's incompleteness theorems using the Isabelle proof assistant is described. This is apparently the first mechanical verification of the second incompleteness theorem. The work closely follows {\'S}wierczkowski…
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
Autonomous systems that operate in a shared environment with people need to be able to follow the rules of the society they occupy. While laws are unique for one society, different people and institutions may use different rules to guide…
We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality…
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…