Related papers: A Variant on the Feline Josephus Problem
Given a number field $K$ that is a subfield of the real numbers, we generalize the notion of the classical Frobenius problem to the ring of integers $\mathfrak{O}_K$ of $K$ by describing certain Frobenius semigroups,…
We study a variant of the Erd\H os unit distance problem, concerning angles between successive triples of points chosen from a large finite point set. Specifically, given a large finite set of $n$ points $E$, and a sequence of angles…
In this paper, we investigate bounded action theories in the situation calculus. A bounded action theory is one which entails that, in every situation, the number of object tuples in the extension of fluents is bounded by a given constant,…
We study a variation of the classical pursuit-evasion game of Cops and Robbers in which agents are required to move to an adjacent vertex on every turn. We explore how the minimum number of cops needed to catch the robber can change when…
Dialogue games are two-player logic games between a Proponent who puts forward a logical formula A as valid or true and an Opponent who disputes this. An advantage of the dialogical approach is that it is a uniform framework from which…
Existential rules, long known as tuple-generating dependencies in database theory, have been intensively studied in the last decade as a powerful formalism to represent ontological knowledge in the context of ontology-based query answering.…
We consider a generalization of the classical 100 Prisoner problem and its variant, involving empty boxes, whereby winning probabilities for a team depend on the number of attempts, as well as on the number of winners. We call this the…
The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes as input a database and a set of constraints, and iteratively…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
We explore the question asking for graphs $G$ for which the total distance decreases, possibly by a fixed constant $k$, upon the removal of any of its vertices. We obtain results leading to intuition and doubts for the \v{S}olt\'es' problem…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
The standard iterated prisoner's dilemma is an unrealistic model of social behaviour because it forces individuals to participate in the interaction. We analyse a model in which players have the option of ending their association. If the…
Recently uncovered second derivative discontinuous solutions of the simplest linear ordinary differential equation define not only an nonstandard extension of the framework of the ordinary calculus, but also provide a dynamical…
We discuss the following folklore problem. On a bookshelf, there are $N$ tomes of the Encyclopedia in random order. Each hour, a librarian takes a tome which stands not on its place, and puts it in its place. Show that the process will…
We study existence and uniqueness of bounded solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the…
This article presents a variant of Fleming-Viot particle systems, which are a standard way to approximate the law of a Markov process with killing as well as related quantities. Classical Fleming-Viot particle systems proceed by simulating…
In order to find Hamiltonian cycle, algorithm should find edges that creates a Hamiltonian cycle. Higher number of edges creates more possibilities to check to solve the problem. Algorithm rests on analysis of original graph and opposite…
Given integer $n$ and $k$ such that $0 < k \leq n$ and $n$ piles of stones, two players alternate turns. By one move it is allowed to choose any $k$ piles and remove exactly one stone from each. The player who has to move but cannot is the…
The chase procedure for existential rules is an indispensable tool for several database applications, where its termination guarantees the decidability of these tasks. Most previous studies have focused on the skolem chase variant and its…
Various voting rules are based on ranking the candidates by scores induced by aggregating voter preferences. A winner (respectively, unique winner) is a candidate who receives a score not smaller than (respectively, strictly greater than)…