Felix Stutz

• Distributed message-passing systems have become ubiquitous and essential for our daily lives. Hence, designing and implementing them correctly is of utmost importance. This is, however, very challenging at the same time. In fact, it is well-known that verifying such systems is algorithmically undecidable in general due to the interplay of asynchronous communication (messages are buffered) and concurrency. When designing communication in a system, it is natural to start with a global protocol specification of the desired communication behaviour. In such a top-down approach, the implementability problem asks, given such a global protocol, if the specified behaviour can be implemented in a distributed setting without additional synchronisation. This problem has been studied from two perspectives in the literature. On the one hand, there are Multiparty Session Types (MSTs) from process algebra, with global types to specify protocols. Key to the MST approach is a so-called projection operator, which takes a global type and tries to project it onto every participant: if successful, the local specifications are safe to use. This approach is efficient but brittle. On the other hand, High-level Message Sequence Charts (HMSCs) study the implementability problem from an automata-theoretic perspective. They employ very few restrictions on protocol specifications, making the implementability problem for HMSCs undecidable in general. The work in this thesis is the first to formally build a bridge between the world of MSTs and HMSCs. To start, we present a generalised projection operator for sender-driven choice. This allows a sender to send to different receivers when branching, which is crucial to handle common communication patterns from distributed computing. Despite this first step, we also show that the classical MST projection approach is inherently incomplete. We present the first formal encoding from global types to HMSCs. With this, we prove decidability of the implementability problem for global types with sender-driven choice. Furthermore, we develop the first direct and complete projection operator for global types with sender-driven choice, using automata-theoretic techniques, and show its effectiveness with a prototype implementation. We are the first to provide an upper bound for the implementability problem for global types with sender-driven (or directed) choice and show it to be in PSPACE. We also provide a session type system that uses the results from our projection operator. Last, we introduce protocol state machines (PSMs) – an automata-based protocol specification formalism – that subsume both global types from MSTs and HMSCs with regard to expressivity. We use transformations on PSMs to show that many of the syntactic restrictions of global types are not restrictive in terms of protocol expressivity. We prove that the implementability problem for PSMs with mixed choice, which requires no dedicated sender for a branch but solely all labels to be distinct, is undecidable in general. With our results on expressivity, this answers an open question: the implementability problem for mixed-choice global types is undecidable in general.