Related papers: Higher-Dimensional Automata : Extension to Infinit…

Let $NFA_b(q)$ denote the set of languages accepted by nondeterministic finite automata with $q$ states over an alphabet with $b$ letters. Let $B_n$ denote the set of words of length $n$. We give a quadratic lower bound on the VC dimension…

We develop a general framework for the specification and implementation of systems whose executions are words, or partial orders, over an infinite alphabet. As a model of an implementation, we introduce class register automata, a one-way…

We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of {\it one-way quantum finite…

Open-vocabulary 3D object detection (OV-3DOD) aims at localizing and classifying novel objects beyond closed sets. The recent success of vision-language models (VLMs) has demonstrated their remarkable capabilities to understand open…

This work is a survey of the main results reported for the degree of extension of two models defining non-regular languages, namely the context-free grammar and the extended automaton over groups. More precisely, we recall the main results…

This note is a survey of various results on the capabilities of unique hard attention transformers encoders (UHATs) to recognize formal languages. We distinguish between masked vs. non-masked, finite vs. infinite image and general vs.…

We develop a new type and effect system based on B\"uchi automata to capture finite and infinite traces produced by programs in a small language which allows non-deterministic choices and infinite recursions. There are two key technical…

Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata…

We introduce a novel automata model, called pebble-intervals automata (PIA), and study its power and closure properties. PIAs are tailored for a decidable fragment of FO that is important for reasoning about structures that use data values…

This paper discusses the theory and algorithms for interacting large language model agents (LLMAs) using methods from statistical signal processing and microeconomics. While both fields are mature, their application to decision-making…

Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages~$L$ that assign to each word~$w$ a real number~$L(w)$. In the case of infinite words, the value of a run is…

There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…

Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we…

We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…

We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean…

First, we show that universality and other properties of general jumping finite automata are undecidable, which answers a question asked by Meduna and Zemek in 2012. Second, we close the study raised by \v{C}erno and Mr\'{a}z in 2010 by…

We investigate higher-dimensional $\Delta$-systems indexed by finite sets of ordinals, isolating a particular definition thereof and proving a higher-dimensional version of the classical $\Delta$-system lemma. We focus in particular on…

We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…

We introduce EMMA, an End-to-end Multimodal Model for Autonomous driving. Built upon a multi-modal large language model foundation like Gemini, EMMA directly maps raw camera sensor data into various driving-specific outputs, including…

Pre-trained and frozen large language models (LLMs) can effectively map simple scene rearrangement instructions to programs over a robot's visuomotor functions through appropriate few-shot example prompting. To parse open-domain natural…