Related papers: Towards a homotopy theory of process algebra
We interpret mathematically the pair (master equation, solution of master equation) up to equivalence, as the pair (a presentation of a free triangular dga T over a combination operad O, dga map of T into C, a dga over O) up to homotopy…
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…
It is shown that a higher-dimensional automaton is hhp-bisimilar to the free symmetric HDA generated by it. Consequently, up to hereditary history-preserving bisimilarity, ordinary HDAs and symmetric HDAs are models of concurrency with the…
We introduce a process algebra that concerns the timed behaviour of distributed systems with a known spatial distribution. This process algebra provides a communication mechanism that deals with the fact that a datum sent at one point in…
The purpose of this paper is to collect the homotopical methods used in the development of the theory of flows initialized by author's paper ``A model category for the homotopy theory of concurrency''. It is presented generalizations of the…
Flows over time generalize classical network flows by introducing a notion of time. Each arc is equipped with a transit time that specifies how long flow takes to traverse it, while flow rates may vary over time within the given edge…
In this paper we focus on concurrent processes built on synchronization by means of futures. This concept is an abstraction for processes based on a main execution thread but allowing to delay some computations. The structure of a general…
For any increasing function $f: {\Bbb N} \rightarrow {\Bbb N}_{\ge 2}$ which takes only finitely many distinct values, a connected finite dimensional algebra $\Lambda$ is constructed, with the property that $\text{fin.dim}_n\, \Lambda =…
We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative algebra…
We study a class of deterministic flows in ${\mathbb R}^{d\times k}$, parametrized by a random matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d}$ with i.i.d. centered subgaussian entries. We characterize the asymptotic behavior of these…
This paper introduces the counterpart of strong bisimilarity for labelled transition systems extended with time-out transitions. It supports this concept through a modal characterisation, congruence results for a standard process algebra…
We introduce hypernode automata as a new specification formalism for hyperproperties of concurrent systems. They are finite automata with nodes labeled with hypernode logic formulas and transitions labeled with actions. A hypernode logic…
The assignment flow is a smooth dynamical system that evolves on an elementary statistical manifold and performs contextual data labeling on a graph. We derive and introduce the linear assignment flow that evolves nonlinearly on the…
The assignment flow recently introduced in the J. Math. Imaging and Vision 58/2 (2017), constitutes a high-dimensional dynamical system that evolves on an elementary statistical manifold and performs contextual labeling (classification) of…
This paper introduces Higher Gauge Flow Models, a novel class of Generative Flow Models. Building upon ordinary Gauge Flow Models (arXiv:2507.13414), these Higher Gauge Flow Models leverage an L$_{\infty}$-algebra, effectively extending the…
In a recent paper, the second author and Joana Cirici proved a theorem that says that given appropriate hypotheses, $n$-formality of a differential graded algebraic structure is equivalent to the existence of a chain-level lift of a…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
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…
We build on a fine-grained analysis of session-based interaction as provided by the linear logic typing disciplines to introduce the SAM, an abstract machine for mechanically executing session-typed processes. A remarkable feature of the…