Related papers: On the Multi-Interval Ulam-R\'enyi Game: for 3 lie…

We investigate the following version of the well-known R\'enyi-Ulam game. Two players - the Questioner and the Responder - play against each other. The Responder thinks of a number from the set $\{1,\ldots,n\}$, and the Questioner has to…

Ulam asked for the maximum number of questions required to determine an integer between one and one million by asking questions whose answer is `Yes' or `No' and where one untruthful answer is allowed. Pelc showed that the number of…

A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for…

We study the nascent setting of online computation with imperfect advice, in which the online algorithm is enhanced by some prediction encoded in the form of a possibly erroneous binary string. The algorithm is oblivious to the advice…

Let $\mbox{interval} + k v$, $\mbox{interval} + k e$, and $\mbox{interval} - k e$ denote the classes of graphs that can be obtained from some interval graph by adding $k$ vertices, adding $k$ edges, and deleting $k$ edges, respectively.…

We consider an extension of the 2-person R\'enyi-Ulam liar game in which lies are governed by a channel $C$, a set of allowable lie strings of maximum length $k$. Carole selects $x\in[n]$, and Paul makes $t$-ary queries to uniquely…

This paper explores special arrangements of clues in $m \times n$ Numbrix puzzles. The maximum number of clues which fails to define an $m \times n$ puzzle is demonstrated for all $m$ and $n$. In addition, a small upper bound on the minimum…

The chase is a fundamental tool for existential rules. Several chase variants are known, which differ on how they handle redundancies possibly caused by the introduction of nulls. Given a chase variant, the halting problem takes as input a…

We establish some upper bounds for the number of integer solutions to the Thue inequality $|F(x , y)| \leq m$, where $F$ is a binary form of degree $n \geq 3$ and with non-zero discriminant $D$, and $m$ is an integer. Our upper bounds are…

The $q$-round Renyi-Ulam pathological liar game with $k$ lies on the set $[n]:=\{1,...,n\}$ is a 2-player perfect information zero sum game. In each round Paul chooses a subset $A\subseteq [n]$ and Carole either assigns 1 lie to each…

A lower bound on the minimum required code length of binary codes is obtained. The bound is obtained based on observing a close relation between the Ulam's liar game and channel coding. In fact, Spencer's optimal solution to the game is…

We investigate the Ramsey numbers $r(I_m, L_n)$ which is the minimal natural number $k$ such that every oriented graph on $k$ vertices contains either an independent set of size $m$ or a transitive tournament on $n$ vertices. Apart from the…

Let k_r(n,m) denote the minimum number of r-cliques in graphs with n vertices and m edges. For r=3,4 we give a lower bound on k_r(n,m) that approximates k_r(n,m) with an error smaller than n^r/(n^2-2m). The solution is based on a constraint…

The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is…

The $k$-majority game is played with $n$ numbered balls, each coloured with one of two colours. It is given that there are at least $k$ balls of the majority colour, where $k$ is a fixed integer greater than $n/2$. On each turn the player…

In this work we study the metric distortion problem in voting theory under a limited amount of ordinal information. Our primary contribution is threefold. First, we consider mechanisms which perform a sequence of pairwise comparisons…

It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…

Let $s(n)$ be the number of nonzero bits in the binary digital expansion of the integer $n$. We study, for fixed $k,\ell,m$, the Diophantine system $$ s(ab)=k, \quad s(a)=\ell,\quad \mbox{and }\quad s(b)=m, $$ in odd integer variables…

We consider the Last-Success-Problem with $n$ independent Bernoulli random variables with parameters $p_i>0$. We improve the lower bound provided by F.T. Bruss for the probability of winning and provide an alternative proof to the one given…

We consider the problem of identifying, from its first $m$ noisy moments, a probability distribution on $[0,1]$ of support $k<\infty$. This is equivalent to the problem of learning a distribution on $m$ observable binary random variables…