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Kleene algebra (KA) is an important tool for reasoning about general program equivalences, with a decidable and complete equational theory. However, KA cannot always prove equivalences between specific programs. For this purpose, one adds…
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…
Large language models (LLMs) enhanced with retrieval augmentation has shown great performance in many applications. However, the computational demands for these models pose a challenge when applying them to real-time tasks, such as…
Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with the development of standards such as XML. In this paper, we…
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of…
This paper proposes an epistemological shift in the analysis of large generative models, replacing the category ''Large Language Models'' (LLM) with that of ''Large Discourse Models'' (LDM), and then with that of Artificial Discursive Agent…
This article introduces an innovative architecture designed to declaratively combine Large Language Models (LLMs) with shared histories, and triggers to identify the most appropriate LLM for a given task. Our approach is general and…
We present probabilistic arithmetic automata (PAAs), a general model to describe chains of operations whose operands depend on chance, along with two different algorithms to exactly calculate the distribution of the results obtained by such…
The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this…
Compact representations of automata are important for efficiency. In this paper, we study methods to compute reduced automata, in which no two states accept the same language. We do this for finitary automata (FA), an abstract definition…
We introduce heap automata, a formalism for automatic reasoning about robustness properties of the symbolic heap fragment of separation logic with user-defined inductive predicates. Robustness properties, such as satisfiability,…
As an alternative to visibly pushdown automata, we introduce visibly recursive automata (VRAs), composed of a set of classical automata that can call each other. VRAs are a strict extension of so-called systems of procedural automata, a…
Given a transition system with an independence relation on the alphabet of labels, one can associate with it a usually very large symmetric higher-dimensional automaton. The purpose of this paper is to show that by choosing an acyclic…
This article introduces the novel framework of max-algebraic hybrid automata as a hybrid modelling language in the max-plus algebra. We show that the modelling framework unifies and extends the switching max-plus linear systems framework…
This paper considers finite-automata based algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this…
A complete deterministic finite (semi)automaton (DFA) with a set of states $Q$ is \emph{completely reachable} if every nonempty subset of $Q$ is the image of the action of some word applied to $Q$. The concept of completely reachable…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
FPGAs provide highly parallel and customizable hardware solutions but are traditionally programmed using low-level Hardware Description Languages (HDLs) like VHDL and Verilog. These languages have a low level of abstraction and require…
We introduce a new formalism of higher-dimensional timed automata, based on van Glabbeek's higher-dimensional automata and Alur's timed automata. We prove that their reachability is PSPACE-complete and can be decided using zone-based…
Dataflow architectures are growing in popularity due to their potential to mitigate the challenges posed by the memory wall inherent to the Von Neumann architecture. At the same time, high-level synthesis (HLS) has demonstrated its efficacy…