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This work is a contribution to the study of rewrite games. Positions are finite words, and the possible moves are defined by a finite number of local rewriting rules. We introduce and investigate taking-and-merging games, that is, where…
$\omega$-regular languages are a natural extension of the regular languages to the setting of infinite words. Likewise, they are recognised by a host of automata models, one of the most important being Alternating Parity Automata (APAs), a…
Modern applications require robots to comply with multiple, often conflicting rules and to interact with the other agents. We present Posetal Games as a class of games in which each player expresses a preference over the outcomes via a…
Simple reference games are of central theoretical and empirical importance in the study of situated language use. Although language provides rich, compositional truth-conditional semantics to facilitate reference, speakers and listeners may…
Arguably, omega-regular languages play an important role as a specification formalism in many approaches to systems monitoring via runtime verification. However, since their elements are infinite words, not every omega-regular language can…
Eva is a neuro-symbolic domain-independent multimodal collaborative dialogue system that takes seriously that the purpose of task-oriented dialogue is to assist the user. To do this, the system collaborates by inferring their intentions and…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
Two-player games on graphs provide the theoretical frame- work for many important problems such as reactive synthesis. While the traditional study of two-player zero-sum games has been extended to multi-player games with several notions of…
We study the parameterized complexity of several positional games. Our main result is that Short Generalized Hex is W[1]-complete parameterized by the number of moves. This solves an open problem from Downey and Fellows' influential list of…
We investigate the proof theory of regular expressions with fixed points, construed as a notation for (omega-)context-free grammars. Starting with a hypersequential system for regular expressions due to Das and Pous, we define its extension…
The Naming Game is a model of non-equilibrium dynamics for the self-organized emergence of a linguistic convention or a communication system in a population of agents with pairwise local interactions. We present an extensive study of its…
We provide a syntactic construction of correlated equilibrium. For any finite game, we study how players coordinate their play on a signal by means of a public strategy whose instructions are expressed in some natural language. Language can…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
Natural languages have been argued to evolve under pressure to efficiently compress meanings into words by optimizing the Information Bottleneck (IB) complexity-accuracy tradeoff. However, the underlying social dynamics that could drive the…
Probabilistic omega-automata are variants of nondeterministic automata for infinite words where all choices are resolved by probabilistic distributions. Acceptance of an infinite input word can be defined in different ways: by requiring…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
We consider ideals and Boolean combinations of ideals. For the regular languages within these classes we give expressively complete automaton models. In addition, we consider general properties of regular ideals and their Boolean…
In this paper we revisit the regular-language representation of game semantics of second-order recursion free Idealized Algol with infinite data types. By using symbolic values instead of concrete ones we generalize the standard notion of…
We define a class of languages of infinite words over infinite alphabets, and the corresponding automata. The automata used for recognition are a generalisation of deterministic Muller automata to the setting of nominal sets. Remarkably,…
Omega-powers of finitary languages are languages of infinite words (omega-languages) in the form V^omega, where V is a finitary language over a finite alphabet X. They appear very naturally in the characterizaton of regular or context-free…