Related papers: Winning Sets of Regular Languages: Descriptional a…
This article studies a biased version of the naming game in which players located on a connected graph interact through successive conversations to bootstrap a common name for a given object. Initially, all the players use the same word B…
Let $a$, $b$, and $n$ be integers with $0<a<b<n$. In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects $a$ chips or $b$ chips. If Alice collects $a$ chips, then Bob collects $b$…
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…
Consider a game where a refereed a referee chooses (x,y) according to a publicly known distribution P_XY, sends x to Alice, and y to Bob. Without communicating with each other, Alice responds with a value "a" and Bob responds with a value…
The language we use over the course of conversation changes as we establish common ground and learn what our partner finds meaningful. Here we draw upon recent advances in natural language processing to provide a finer-grained…
The language competition model of Viviane de Oliveira et al is modified by associating with each language a string of 32 bits. Whenever a language changes in this Viviane model, also one randomly selected bit is flipped. If then only…
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…
As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…
We present a new algebraic characterisation of Eve-positionality for $\omega$-regular languages. It involves only a limited number of elementary local properties to be checked. An $\omega$-regular language is Eve-positional if, in all games…
The set of finite words over a well-quasi-ordered set is itself well-quasi-ordered. This seminal result by Higman is a cornerstone of the theory of well-quasi-orderings and has found numerous applications in computer science. However, this…
One of the key concepts in testing is that of adequate test sets. A test selection criterion decides which test sets are adequate. In this paper, a language schema for specifying a large class of test selection criteria is developed; the…
We investigate two problems for a class C of regular word languages. The C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two…
We explain how certain tools from convex analysis and probability theory may be used in order to obtain counting results for the number of words with prescribed frequencies of letters in regular languages.
When flipping a fair coin, let $W = L_1L_2...L_N$ with $L_i\in\{H,T\}$ be a binary word of length $N=2$ or $N=3$. In this paper, we establish second- and third-order linear recurrence relations and their generating functions to discuss the…
We present a new characteristic of a regular ideal language called reset complexity. We find some bounds on the reset complexity in terms of the state complexity of a given language. We also compare the reset complexity and the state…
We examine a variant of the Naming Game, where agents having several words communicate more often than single-word agents. Depending on the preference and dimensionality, the model either converges to a single-language state as in an…
In combinatorial game theory, the winning player for a position in normal play is analyzed and characterized via algebraic operations. Such analyses define a value for each position, called a game value. A game (ruleset) is called universal…
Given an order of the underlying alphabet we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one \emph{and}…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or…