Related papers: A note on Thue games
We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that…
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We…
Language models typically tokenize text into subwords, using a deterministic, hand-engineered heuristic of combining characters into longer surface-level strings such as 'ing' or whole words. Recent literature has repeatedly shown the…
We consider one-round games between a classical referee and two players. One of the main questions in this area is the parallel repetition question: Is there a way to decrease the maximum winning probability of a game without increasing the…
Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis. Optimal strategies may require randomisation when dealing with inherently…
In this paper we study the enumeration and the construction, according to the number of ones, of particular binary words avoiding a fixed pattern. The growth of such words can be described by particular jumping and marked succession rules.…
The article describes a model of automatic analysis of puns, where a word is intentionally used in two meanings at the same time (the target word). We employ Roget's Thesaurus to discover two groups of words which, in a pun, form around two…
Generalizing a problem posed by Cover, we propose an adversarial game in which a permutation is incrementally constructed in a setting of partial information. As in the secretary problem, this permutation is exposed in stages via the…
This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form…
We study the problem of adversarial language games, in which multiple agents with conflicting goals compete with each other via natural language interactions. While adversarial language games are ubiquitous in human activities, little…
Graph grammars form an interesting area of research because of their versatility in modelling diverse situations with graphs as the structures which are to be manipulated. A new class of graph grammars, nc-eNCE Graph Grammars has been…
We modify the game Fuchino, Koppelberg, and Shelah used to characterize the $\kappa$-Freese-Nation property for a given Boolean algebra $A$, replacing players I and II each with a team of $n$ players with limited information. We show that…
We investigate the value of parallel repetition of one-round games with any number of players $k\ge 2$. It has been an open question whether an analogue of Raz's Parallel Repetition Theorem holds for games with more than two players, i.e.,…
This paper presents a mathematical method of playing the puzzle game Wordle. In Wordle, the player has six tries to guess a secret word. After each guess the player is told how their guess compares to the secret word. With the available…
Word embedding, which encodes words into vectors, is an important starting point in natural language processing and commonly used in many text-based machine learning tasks. However, in most current word embedding approaches, the similarity…
Consider the following one-player game played on an initially empty graph with $n$ vertices. At each stage a randomly selected new edge is added and the player must immediately color the edge with one of $r$ available colors. Her objective…
Writers, poets, singers usually do not create their compositions in just one breath. Text is revisited, adjusted, modified, rephrased, even multiple times, in order to better convey meanings, emotions and feelings that the author wants to…
We investigate a class of reinforcement learning dynamics where players adjust their strategies based on their actions' cumulative payoffs over time - specifically, by playing mixed strategies that maximize their expected cumulative payoff…
Two words are $k$-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most $k$ with the same multiplicities. This is a refinement of both abelian equivalence and the Simon congruence. The…
We consider an abstraction of computational security in password protected systems where a user draws a secret string of given length with i.i.d. characters from a finite alphabet, and an adversary would like to identify the secret string…