Related papers: The parallel composition of processes
A derived operation is a bilinear operation on a commutative associative algebra $A$ defined intrinsically out of its product and several derivations of the product. We show that operators of left (or right) multiplications of a derived…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\mathcal{O}\rightarrow\mathcal{P}$ describes a functor allowing a…
Canonical extension of finitary ordered structures such as lattices, posets, proximity lattices, etc., is a certain completion which entirely describes the topological dual of the ordered structure and it does so in a purely algebraic and…
We present a process algebra aimed at describing interactions that are multiparty, i.e. that may involve more than two processes and that are open, i.e. the number of the processes they involve is not fixed or known a priori. Here we focus…
Simple optics are defined using actions of monoidal categories. Compound optics arise, for instance, as natural transformations between polynomial functors. Since a monoidal category is a special case of a bicategory, we formulate complex…
A rigorous derivation is provided for canonical correlations and partial canonical correlations for certain Hilbert space indexed stochastic processes. The formulation relies on a key congruence mapping between the space spanned by a second…
Choreography automata are an automata-based model of choreographies, that we show to be a compositional one. Choreography automata represent global views of choreographies (and rely on the well-known model of communicating finite-state…
We present GraSSP, a novel approach to perform automated parallelization relying on recent advances in formal verification and synthesis. GraSSP augments an existing sequential program with an additional functionality to decompose data…
In the context of security protocol parallel composition, where messages belonging to different protocols can intersect each other, we introduce a new paradigm: term-based composition (i.e. the composition of message components also known…
It is common to encounter symmetric monoidal categories $\mathcal{C}$ for which every object is equipped with an algebraic structure, in a way that is compatible with the monoidal product and unit in $\mathcal{C}$. We define this formally…
Classical Processes (CP) is a calculus where the proof theory of classical linear logic types communicating processes with mobile channels, a la pi-calculus. Its construction builds on a recent propositions as types correspondence between…
An arbitrary linear relation (multivalued operator) acting from one Hilbert space to another Hilbert space is shown to be the sum of a closable operator and a singular relation whose closure is the Cartesian product of closed subspaces.…
A quantitative representation of discourse structure can be computed by measuring lexical cohesion relations among adjacent blocks of text. These representations have been proposed to deal with sub-topic text segmentation. In a parallel…
We extend the free cornering of a symmetric monoidal category, a double categorical model of concurrent interaction, to support branching communication protocols and iterated communication protocols. We validate our constructions by showing…
Kahn process networks are a model of computation based on a collection of sequential, deterministic processes that communicate by sending messages through unbounded channels. They are well suited for modelling stream-based computations, but…
Process algebra CSP only permits a process to engage in one event on a moment and records this single event into the traces of the process. CSP cannot process events simultaneously, it treat the events occurred simultaneously as one single…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
We study diverse parametrized versions of the operad of associative algebra, where the parameter are taken in an associative semigroup $\Omega$ (generalization of matching or family associative algebras) or in its cartesian square…
We survey some basic mathematical structures, which arguably are more primitive than the structures taught at school. These structures are orders, with or without composition, and (symmetric) monoidal categories. We list several `real life'…