Related papers: A determinacy approach to Borel combinatorics
Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. In this…
Given a truncated perturbation expansion of a physical quantity, one can, under certain circumstances, obtain lower or upper bounds (or both) to the sum of the full perturbation series by using the Borel transform and a variational…
We show a model construction for a system of higher-order illative combinatory logic $\mathcal{I}_\omega$, thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
Cooperative interval games are a generalized model of cooperative games in which the worth of every coalition corresponds to a closed interval representing the possible outcomes of its cooperation. Selections are all possible outcomes of…
This survey of methods surrounding lattice point methods for binomial ideals begins with a leisurely treatment of the geometric combinatorics of binomial primary decomposition. It then proceeds to three independent applications whose…
In this paper we define the canonical mixed extension of a decision form game. We motivate the necessity to introduce this concept and we show several examples about the new concept. In particular we focus our study upon the mixed…
Hex is a well known connection game in which two players attempt to connect opposite sides of the board by colored stones. In 2022, Hamkins and Leonessi introduced an infinite version, in which the goal is to construct a certain kind of…
We investigate the relation between Bell inequalities and nonlocal games by presenting a systematic method for their bilateral conversion. In particular, we show that while to any nonlocal game there naturally corresponds a unique Bell…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
We provide a gentle introduction, aimed at non-experts, to Borel combinatorics that studies definable graphs on topological spaces. This is an emerging field on the borderline between combinatorics and descriptive set theory with deep…
Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special functions and not only. The use of integral transforms of Borel…
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…
The monadic theory of $(\mathbb R,\le)$ with quantification restricted to Borel sets is decidable. The Boolean combinations of $F_\sigma$ sets form an elementary substructure of the Borel sets. Under determinacy hypotheses, the proof…
In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: 1. Some…
Our paper explores the game theoretic value of the 7-in-a-row game. We reduce the problem to solving a finite board game, which we target using Proof Number Search. We present a number of heuristic improvements to Proof Number Search and…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…