Section: New Results

Languages for composition

Participants : Axel Legay, Thomas Given-Wilson.

This part is concerned with Task 1, especially to describe the composition of complex systems, and to study expressivity of existing formalisms.

Contemporary cyber-physical systems are inherently constructed out of a variety of agents with communication and interaction forming a key role in the behaviour of the system as a whole. Traditional approaches to reasoning over a single computation or treating the system as a single agent prove unsatisfactory for understanding the capabilities, strengths, and weaknesses of such systems.

Since communication is a fundamental to such systems it is necessary to understand the role the communication primitives themselves play. There are many approaches to communication primitives, often chosen for their ability to easily represent desired behaviour. However, the formal properties of many implementations or chosen models have not been presented.

An alternative to formalising each possible model individually is to abstract away and reason over families of models based on their communication primitives. This allows keys results to be achieved in one model, and then generalised to the entire family, or transferred to other families based upon formal relations between these families. Thus making it possible for results to be easily applied to many models or systems without repeating significant effort.

Papers:

[20] (C), [32] (J; submitted)

The expressiveness of communication primitives has been explored in a common framework based on the π-calculus by considering four features: synchronism (asynchronous vs synchronous), arity (monadic vs polyadic data), communication medium (shared dataspaces vs channel-based), and pattern-matching (binding to a name vs testing name equality vs intensionality). Here another dimension coordination is considered that accounts for the number of processes required for an interaction to occur. Coordination generalises binary languages such as π-calculus to joining languages that combine inputs such as the Join Calculus and general rendezvous calculus. By means of possibility/impossibility of encodings, this paper shows coordination is unrelated to the other features. That is, joining languages are more expressive than binary languages, and no combination of the other features can encode a joining language into a binary language. Further, joining is not able to encode any of the other features unless they could be encoded otherwise.

[33] (C; submitted)

The expressiveness of communication primitives has been explored in a common framework by considering four features: synchronism, arity, communication medium, and pattern-matching. These all assume asymmetric communication between input and output primitives, however some calculi consider more symmetric approaches to communication such as fusion calculus and Concurrent Pattern Calculus. Symmetry can be considered either as allowing a mixture of input and output in an action or co-action, or as the unification of actions. By means of possibility/impossibility of encodings, this paper shows that: the action and co-action approach is related to or more expressive than many previously considered languages; and the unification approach is more expressive than some, but mostly unrelated to other languages.