Subtyping is a crucial ingredient of session type theory and its applications, notably to programming language implementations. In this paper, we study effective ways to check whether a session type is a subtype of another by applying a characteristic formulae approach to the problem. Our core contribution is an algorithm to generate a modal mu-calculus formula that characterises all the supertypes (or subtypes) of a given type. Subtyping checks can then be off-loaded to model checkers, thus incidentally yielding an efficient algorithm to check safety of session types, soundly and completely. We have implemented our theory and compared its cost with other classical subtyping algorithms.
We propose a typing theory, based on multiparty session types, for modular verification of real-time choreographic interactions. To model real-time implementations, we introduce a simple calculus with delays and a decidable static proof system. The proof system ensures type safety and time-error freedom, namely processes respect the prescribed timing and causalities between interactions. A decidable condition on timed global types guarantees time-progress for validated processes with delays, and gives a sound and complete characterisation of a new class of CTAs with general topologies that enjoys progress and liveness. Design by Contract (DbC) promotes reliable software development through elaboration of type signatures for sequential programs with logical predicates. This paper presents an assertion method, based on the π-calculus with full recursion, which generalises the notion of DbC to multiparty distributed interactions to enable effective specification and verification of distributed multiparty protocols. Centring on global assertions and their projections onto endpoint assertions, our method allows clear specifications for typed sessions, constraining the content of the exchanged messages, the choice of sub-conversations to follow, and invariants on recursions. The paper presents key theoretical foundations of this framework, including a sound and relatively complete compositional proof system for verifying processes against assertions.  Graphical choreographies, or global graphs, are general multiparty session specifications featuring expressive constructs such as forking, merging, and joining for representing application-level protocols. Global graphs can be directly translated into modelling notations such as BPMN and UML. This paper presents an algorithm whereby a global graph can be constructed from asynchronous interactions represented by communicating finite-state machines (CFSMs). Our results include: a sound and complete characterisation of a subset of safe CFSMs from which global graphs can be constructed; an algorithm to translate CFSMs to global graphs; a time complexity analysis; and an implementation of our theory, as well as an experimental evaluation. Subtyping in concurrency has been extensively studied since early 1990s as one of the most interesting issues in type theory. The correctness of subtyping relations has been usually provided as the soundness for type safety. The converse direction, the completeness, has been largely ignored in spite of its usefulness to define the greatest subtyping relation ensuring type safety. This paper formalises preciseness (i.e. both soundness and completeness) of subtyping for mobile processes and studies it for the synchronous and the asynchronous session calculi. We first prove that the well-known session subtyping, the branching-selection subtyping, is sound and complete for the synchronous calculus. Next we show that in the asynchronous calculus, this subtyping is incomplete for type-safety: that is, there exist session types T and S such that T can safely be considered as a subtype of S, but T ≤ S is not derivable by the subtyping. We then propose an asynchronous subtyping system which is sound and complete for the asynchronous calculus. The method gives a general guidance to design rigorous channel-based subtypings respecting desired safety properties. This paper studies safety, progress, and non-zeno properties of Communicating Timed Automata (CTAs), which are timed automata (TA) extended with unbounded communication channels, and presents a procedure to build timed global specifications from systems of CTAs. We define safety and progress properties for CTAs by extending properties studied in communicating finite-state machines to the timed setting. We then study non-zenoness for CTAs; our aim is to prevent scenarios in which the participants have to execute an infinite number of actions in a finite amount of time. We propose sound and decidable conditions for these properties, and demonstrate the practicality of our approach with an implementation and experimental evaluations of our theory.