Related papers: Algebraic properties of structured context-free la…
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…
Logic programs with aggregates (LPA) are one of the major linguistic extensions to Logic Programming (LP). In this work, we propose a generalization of the notions of unfounded set and well-founded semantics for programs with monotone and…
The paper explains the connection between topological theories for one-manifolds with defects and values in the Boolean semiring and automata and their generalizations. Finite state automata are closely related to regular languages. To each…
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
Automata models for data languages (i.e. languages over infinite alphabets) often feature either global or local freshness operators. We show that Bollig et al.'s session automata, which focus on global freshness, are equivalent to regular…
Linear attention methods offer a compelling alternative to softmax attention due to their efficiency in recurrent decoding. Recent research has focused on enhancing standard linear attention by incorporating gating while retaining its…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
With the introduction of transformer-based models for vision and language tasks, such as LLaVA and Chameleon, there has been renewed interest in the discrete tokenized representation of images. These models often treat image patches as…
Many natural language processing systems operate over tokenizations of text to address the open-vocabulary problem. In this paper, we give and analyze an algorithm for the efficient construction of deterministic finite automata (DFA)…
Pretrained vision-language models (VLMs) can make semantic and visual inferences across diverse settings, providing valuable common-sense priors for robotic control. However, effectively grounding this knowledge in robot behaviors remains…
Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary…
Pattern matching is a popular feature in functional, imperative and object-oriented programming languages. Language designers should therefore invest effort in a good design for pattern matching. Most languages choose a first-match…
Input-driven pushdown automata with translucent input letters are investigated. Here, the use of translucent input letters means that the input is processed in several sweeps and that, depending on the current state of the automaton, some…
Since the early Sixties and Seventies it has been known that the regular and context-free languages are characterized by definability in the monadic second-order theory of certain structures. More recently, these descriptive…
A $\lambda$-graph system is a labeled Bratteli diagram with some additional structure, which presents a subshift and yields a $C^*$-algebra. In this paper, we construct a $\lambda$-graph system from a pushdown automaton, such that the…
Cellular automata (CA) are well-studied models of decentralized parallel computation, known for their ability to exhibit complex global behavior from simple local rules. While their dynamics have been widely explored through simulations, a…
We introduce session automata, an automata model to process data words, i.e., words over an infinite alphabet. Session automata support the notion of fresh data values, which are well suited for modeling protocols in which sessions using…
The article defines and studies the genus of finite state deterministic automata (FSA) and regular languages. Indeed, a FSA can be seen as a graph for which the notion of genus arises. At the same time, a FSA has a semantics via its…
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,…
We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of…