Related papers: Core Higher-Order Session Processes: Tractable Equ…
A famous result due to Ko and Friedman (1982) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sense. Yet, both functionals are routinely computed at great…
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in…
We define a novel calculus that combines a call-by-name functional core with session-based communication primitives. We develop a typing discipline that guarantees both normalisation of expressions and progress of processes and that…
We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal)…
Suppose $(G,G')$ is a dual pair of subgroups of a metaplectic group. The dual pair correspondence is a bijection between (subsets of the) irreducible representations of $G$ and $G'$, defined by the non-vanishing of…
What makes two computational systems equivalent? Topos theory answers with classifying toposes: a system's semantic content is encoded in the geometric theory it classifies, and two presentations are equivalent when their classifying…
We present a type system to guarantee termination of pi-calculus processes that exploits input/output capabilities and subtyping, as originally introduced by Pierce and Sangiorgi, in order to analyse the usage of channels. We show that our…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators $H=\sum_k A_k$, for…
This work introduces a parametric simulation-free reduced order model for incompressible flows undergoing a Hopf bifurcation, leveraging the parametrisation method for invariant manifolds. Unlike data-driven approaches, this method operates…
Cohesive powers of computable structures can be viewed as effective ultraproducts over effectively indecomposable sets called cohesive sets. We investigate the isomorphism types of cohesive powers $\Pi _{C}% \mathcal{L}$ for familiar…
This paper proposes a novel higher-order multi-scale (HOMS) computational method, which is highly targeted for efficient, high-accuracy and low-computational-cost simulation of hygro-thermo-mechanical (H-T-M) coupling problems in…
Existing formalisms for the algebraic specification and representation of networks of reversible agents suffer some shortcomings. Despite multiple attempts, reversible declensions of the Calculus of Communicating Systems (CCS) do not offer…
This paper aims to improve the performance of large language models by addressing the variable computational demands in inference steps, where some tokens require more computational resources than others. We present HARP, a simple…
This paper is an extended version of our work in \cite{Ca2025}. We extend the concept of effective reducibility between statements of set theory with ordinal Turing machines (OTMs) explored in \cite{Ca2018} for $\Pi_{2}$-statements to…
The $\pi$-calculus is used as a model for programming languages. Its contexts exhibit arbitrary concurrency, making them very discriminating. This may prevent validating desirable behavioural equivalences in cases when more disciplined…
Lie-Trotter-Suzuki decompositions are an efficient way to approximate operator exponentials $\exp(t H)$ when $H$ is a sum of $n$ (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution…
We define a pi-calculus variant with a costed semantics where channels are treated as resources that must explicitly be allocated before they are used and can be deallocated when no longer required. We use a substructural type system…
In this work, we incorporate reversibility into structured communication-based programming, to allow parties of a session to automatically undo, in a rollback fashion, the effect of previously executed interactions. This permits taking…