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In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…
Classical countably additive real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the same probability value -- namely, zero -- to cases that are impossible as well as to cases that are possible.…
Multi-way tables with specified marginals arise in a variety of applications in statistics and operations research. We provide a comprehensive complexity classification of three fundamental computational problems on tables: existence,…
Although hypothesis tests play a prominent role in Science, their interpretation can be challenging. Three issues are (i) the difficulty in making an assertive decision based on the output of an hypothesis test, (ii) the logical…
This paper presents a solution to the Knights and Spies Problem: In a room there are n people, each labelled with a unique number between 1 and n. A person may either be a knight or a spy. Knights always tell the truth, while spies may…
Discuss several tricks for solving twenty question problems which in this paper is depicted as a guessing game. Player tries to find a ball in twenty boxes by asking as few questions as possible, and these questions are answered by only…
In this paper we study the Three Hat Problem which appeared in Puzzle Corner of the Technology Review magazine. This puzzle gives a scenario in which three players wearing hats are sitting together and each hat can be seen by everyone…
Backdoors of answer-set programs are sets of atoms that represent clever reasoning shortcuts through the search space. Assignments to backdoor atoms reduce the given program to several programs that belong to a tractable target class.…
The Sliding Window Secretary Problem allows a window of choices to the Classical Secretary Problem, in which there is the option to choose the previous $K$ choices immediately prior to the current choice. We consider a case of this…
In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures.…
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
AI-driven outcomes can be challenging for end-users to understand. Explanations can address two key questions: "Why this outcome?" (factual) and "Why not another?" (counterfactual). While substantial efforts have been made to formalize…
Humanity has been fascinated by the pursuit of fortune since time immemorial, and many successful outcomes benefit from strokes of luck. But success is subject to complexity, uncertainty, and change - and at times becoming increasingly…
An overview is presented of recent work on some statistical problems on multiparticle random walks. We consider a Euclidean, deterministic fractal or disordered lattice and N >> 1 independent random walkers initially (t=0) placed onto the…
For a triangle $\Delta$, let (P) denote the problem of the existence of points in the plane of $\Delta$, that are at rational distance to the 3 vertices of $\Delta$. Answer to (P) is known to be positive in the following situation: $\Delta$…
We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…
We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted,…
We consider training probabilistic classifiers in the case of a large number of classes. The number of classes is assumed too large to perform exact normalisation over all classes. To account for this we consider a simple approach that…
In this paper we solve the three-player-game question. A three-player-game consists of a series of rounds. There are altogether three players. Two players participate in each round, at the end of the round the loser quits and the third…
Selection of input features such as relevant pieces of text has become a common technique of highlighting how complex neural predictors operate. The selection can be optimized post-hoc for trained models or incorporated directly into the…