A non-interleaving process calculus for multi-party synchronisation

We introduce the wire calculus. Its dynamic features are inspired by Milner's CCS: a unary prefix operation, binary choice and a standard recursion construct. Instead of an interleaving parallel composition operator there are operators for synchronisation along a common boundary and non-communicating parallel composition. The (operational) semantics is a labelled transition system obtained with SOS rules. Bisimilarity is a congruence with respect to the operators of the language. Quotienting terms by bisimilarity results in a compact closed category

A Note on the Expressiveness of BIP

We extend our previous algebraic formalisation of the notion of component-based framework in order to formally define two forms, strong and weak, of the notion of full expressiveness. Our earlier result shows that the BIP (Behaviour-Interaction-Priority) framework does not possess the strong full expressiveness. In this paper, we show that BIP has the weak form of this notion and provide results detailing weak and strong full expressiveness for classical BIP and several modifications, obtained by relaxing the constraints imposed on priority models.Comment: In Proceedings EXPRESS/SOS 2016, arXiv:1608.0269

Extended Connectors: Structuring Glue Operators in BIP

Based on a variation of the BIP operational semantics using the offer predicate introduced in our previous work, we extend the algebras used to model glue operators in BIP to encompass priorities. This extension uses the Algebra of Causal Interaction Trees, T(P), as a pivot: existing transformations automatically provide the extensions for the Algebra of Connectors. We then extend the axiomatisation of T(P), since the equivalence induced by the new operational semantics is weaker than that induced by the interaction semantics. This extension leads to canonical normal forms for all structures and to a simplification of the algorithm for the synthesis of connectors from Boolean coordination constraints.Comment: In Proceedings ICE 2013, arXiv:1310.401

Bialgebraic Semantics for String Diagrams

Turi and Plotkin's bialgebraic semantics is an abstract approach to specifying the operational semantics of a system, by means of a distributive law between its syntax (encoded as a monad) and its dynamics (an endofunctor). This setup is instrumental in showing that a semantic specification (a coalgebra) satisfies desirable properties: in particular, that it is compositional. In this work, we use the bialgebraic approach to derive well-behaved structural operational semantics of string diagrams, a graphical syntax that is increasingly used in the study of interacting systems across different disciplines. Our analysis relies on representing the two-dimensional operations underlying string diagrams in various categories as a monad, and their bialgebraic semantics in terms of a distributive law over that monad. As a proof of concept, we provide bialgebraic compositional semantics for a versatile string diagrammatic language which has been used to model both signal flow graphs (control theory) and Petri nets (concurrency theory). Moreover, our approach reveals a correspondence between two different interpretations of the Frobenius equations on string diagrams and two synchronisation mechanisms for processes, \`a la Hoare and \`a la Milner.Comment: Accepted for publications in the proceedings of the 30th International Conference on Concurrency Theory (CONCUR 2019

Connector algebras for C/E and P/T nets interactions

A quite fourishing research thread in the recent literature on component based system is concerned with the algebraic properties of different classes of connectors. In a recent paper, an algebra of stateless connectors was presented that consists of five kinds of basic connectors, namely symmetry, synchronization, mutual exclusion, hiding and inaction, plus their duals and it was shown how they can be freely composed in series and in parallel to model sophisticated "glues". In this paper we explore the expressiveness of stateful connectors obtained by adding one-place buffers or unbounded buffers to the stateless connectors. The main results are: i) we show how different classes of connectors exactly correspond to suitable classes of Petri nets equipped with compositional interfaces, called nets with boundaries; ii) we show that the difference between strong and weak semantics in stateful connectors is reflected in the semantics of nets with boundaries by moving from the classic step semantics (strong case) to a novel banking semantics (weak case), where a step can be executed by taking some "debit" tokens to be given back during the same step; iii) we show that the corresponding bisimilarities are congruences (w.r.t. composition of connectors in series and in parallel); iv) we show that suitable monoidality laws, like those arising when representing stateful connectors in the tile model, can nicely capture concurrency aspects; and v) as a side result, we provide a basic algebra, with a finite set of symbols, out of which we can compose all P/T nets, fulfilling a long standing quest

Offer Semantics: Achieving Compositionality, Flattening and Full Expressiveness for the Glue Operators in BIP

Based on a concise but comprehensive overview of some fundamental properties required from component-based frameworks, namely compositionality, incrementality, flattening, modularity and expressiveness, we review three modifications of the semantics of glue operators in the Behaviour-Interaction-Priority (BIP) framework. We provide theoretical results and examples illustrating the degree, to which the three semantics meet these requirements. In particular, we show that the latest semantics, based on the offer predicate is the only one that satisfies all of them. The classical and offer semantics are not comparable: there are systems that can be assembled in the classical semantics, but not in the offer one. We present a strict characterisation of the behaviour hierarchy determining the conditions, under which systems in the classical semantics can be transposed into the offer semantics directly, with minor modifications, by introducing a new type of synchronisation or not at all. The offer semantics allows us to extend the algebras, which are used to model glue operators in BIP, to encompass priorities. This extension uses the Algebra of Causal Interaction Trees, T(P), as a pivot: existing transformations automatically provide the extensions for the Algebra of Connectors. We then extend the axiomatisation of T(P), since the equivalence induced by the new operational semantics is weaker than that induced by the interaction semantics. This extension leads to canonical normal forms for all structures and to a simplification of the algorithm for the synthesis of connectors from Boolean coordination constraints

A Semantic Framework for Architecture Modelling

Architectures are common means for organising coordination between components in order to build complex systems and to make them manageable. They allow thinking on a higher plane and avoiding low-level mistakes. Architectures provide means for ensuring correctness-by-construction by enforcing global properties characterising the coordination between components. In this work, we consider the following questions of architecture modelling: 1) how to model architectures; 2) how to compose them if several properties enforced by different architectures are required; 3) how to specify architectures styles that generalise the notion of architectures and represent families of architectures satisfying the same property. An architecture can be considered as an operator that, applied to a set of components, builds a composite component meeting a characteristic property. The underlying concepts of components and their interaction originate from the BIP framework. This thesis is structured in two parts. In the first part, we study the expressiveness of glue operators in the BIP framework. We provide results for classical BIP glue and for several modifications obtained by relaxing the constraints imposed on priority models. We also study an alternative semantics of BIP glue based on the offer predicate. It meets fundamental properties required from component-based frameworks, namely compositionality, incrementality, flattening and modularity. We provide the comparison with the classical BIP semantics and the algorithm for the synthesis of connectors from the interaction logic used to describe coordination constraints. In the second part, we define architectures and propose an architecture composition operator. We study their properties and prove that the composition operator preserves safety properties of its operands. The alternative glue semantics presented in the first part of the thesis allows to extend architectures with priorities. For the specification of architecture styles, we propose configuration logics. We provide a sound and complete axiomatisation of the propositional configuration logic as well as decision procedures for checking that an architecture satisfies a given logical specification. To allow genericity of specifications, we study higher-order extensions of the propositional configuration logic. We illustrate with examples the specification of various architecture styles. We provide an experimental evaluation using the Maude rewriting system to implement the decision procedure for configuration logics. Additionally, we study the relation between the architecture composition operator and the composition of configuration logic formulas