Related papers: The parallel composition of processes

In this paper, we described the GAP implementation of crossed modules of commutative algebras and cat$^{1}$-algebras and their equivalence.

Classical approaches like process algebras or labelled transition systems deal with static composition to model non-trivial concurrent or distributed systems; this is not sufficient for systems with dynamic architecture and with variable…

Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide.…

This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…

We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on…

This paper consists of $3$ parts. The first part only considers classical processes and introduces two different extensions of the notion of hidden Markov process. In the second part, the notion of quantum hidden process is introduced. In…

This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…

Usage of multiprocessor and multicore computers implies parallel programming. Tools for preparing parallel programs include parallel languages and libraries as well as parallelizing compilers and convertors that can perform automatic…

We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…

We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…

We give the definition of presentations of linear monoidal categories. Our main result is that given a presentation of a linear monoidal category, we can produce a presentation of the same category as a linear category. We apply this result…

We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable conditions (including that M forms a factorization system),…

The logical parallelism of propositional connectives and type constructors extends beyond the static realm of predicates, to the dynamic realm of processes. Understanding the logical parallelism of process propositions and dynamic types was…

Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…

The main result of this paper is the construction of a trace and a trace pairing for endomorphisms satisfying suitable conditions in a monoidal category. This construction is a common generalization of the trace for endomorphisms of…

In this paper, we consider the groupoidification of the fermion algebra. We construct a groupoid as the categorical analogues of the fermionic Fock space, and the creation and annihilation operators correspond to spans of groupoids. The…

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…

In the theory of coalgebras, trace semantics can be defined in various distinct ways, including through algebraic logics, the Kleisli category of a monad or its Eilenberg-Moore category. This paper elaborates two new unifying ideas: 1)…

For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…

In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since…