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We present a Curry-style second-order type system with union and intersection types for the lambda-calculus with constructors of Arbiser, Miquel and Rios, an extension of lambda-calculus with a pattern matching mechanism for variadic…

This paper shows that the recent approach to quantitative typing systems for programming languages can be extended to pattern matching features. Indeed, we define two resource aware type systems, named U and E, for a lambda-calculus…

We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…

A substantial amount of research has been carried out in developing machine learning algorithms that account for term dependence in text classification. These algorithms offer acceptable performance in most cases but they are associated…

Large language models (LLMs) are increasingly explored for their reasoning capabilities, yet their ability to perform structured, constraint-based optimization from natural language remains insufficiently understood. This study evaluates…

The use of spatio-temporal logics in control is motivated by the need to impose complex spatial and temporal behavior on dynamical systems, and to control these systems accordingly. Synthesizing correct-by-design control laws is a…

This paper establishes relative expressiveness results for several modal mu-calculi interpreted over timed automata. These mu-calculi combine modalities for expressing passage of (real) time with a general framework for defining formulas…

LS is a particular type of computational processes simulating living tissue. They use an unlimited branching process arising from the simultaneous substitutions of some words instead of letters in some initial word. This combines the…

Large eliminations provide an expressive mechanism for arity- and type-generic programming. However, as large eliminations are closely tied to a type theory's primitive notion of inductive type, this expressivity is not expected within…

We describe a system for building task-oriented dialogue systems combining the in-context learning abilities of large language models (LLMs) with the deterministic execution of business logic. LLMs are used to translate between the surface…

The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…

We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…

This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one…

In this paper we introduce a typed, concurrent $\lambda$-calculus with references featuring explicit substitutions for variables and references. Alongside usual safety properties, we recover strong normalization. The proof is based on a…

Cascade systems route computational requests to smaller models when possible and defer to larger models only when necessary, offering a promising approach to balance cost and quality in LLM deployment. However, they face a fundamental…

For an interacting spatio-temporal lattice system we introduce a formal way of expressing multi-time correlation functions of local observables located at the same spatial point with a time state, i.e. a statistical distribution of…

We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the…

This paper presents a novel application of large language models in user simulation for task-oriented dialog systems, specifically focusing on an in-context learning approach. By harnessing the power of these models, the proposed approach…

Proofs by logical relations play a key role to establish rich properties such as normalization or contextual equivalence. They are also challenging to mechanize. In this paper, we describe the completeness proof of algorithmic equality for…

Spatio-temporal forecasting plays a crucial role in various sectors such as transportation systems, logistics, and supply chain management. However, existing methods are limited by their ability to handle large, complex datasets. To…