We present a novel approach to compare process calculi and their synchronisation mechanisms by using synchronisation patterns and explicitly considering the degree of distributability. For this, we propose a new quality criterion that (1) measures the preservation of distributability and (2) allows us to derive two synchronisation patterns that separate several variants of pi-like calculi. Precisely, we prove that there is no good and distributability-preserving encoding from the synchronous pi-calculus with mixed choice into its fragment with only separate choice, and neither from the asynchronous pi-calculus (without choice) into the join-calculus.

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This technical report contains the proofs to the lemmata and theorems of [PN12] as well as some additional material. As main contributions [PN12] presents an encoding of mixed choice in the context of the π-calculus and a criterion to measure whether the degree of distribution in process networks is preserved.

Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with quality criteria. There exists a bunch of different criteria and different variants of criteria in order to reason in different settings. This leads to incomparable results. Moreover it is not always clear whether the criteria used to obtain a result in a particular setting do indeed fit to this setting. We show how to formally reason about and compare encodability criteria by mapping them on requirements on a relation between source and target terms that is induced by the encoding function. In particular we analyse the common criteria full abstraction, operational correspondence, divergence reflection, success sensitiveness, and respect of barbs; e.g. we analyse the exact nature of the simulation relation (coupled simulation versus bisimulation) that is induced by different variants of operational correspondence. This way we reduce the problem of analysing or comparing encodability criteria to the better understood problem of comparing relations on processes.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.06347. The Isabelle/HOL source files, and a full proof document, are available in the Archive of Formal Proofs, at http://afp.sourceforge.net/entries/Encodability_Process_Calculi.shtm

We strive to use session type technology to prove behavioural properties of fault-tolerant distributed algorithms. Session types are designed to abstractly capture the structure of (even multi-party) communication protocols. The goal of session types is the analysis and verification of the protocols' behavioural properties. One important such property is progress, i.e., the absence of (unintended) deadlock. Distributed algorithms often resemble (compositions of) multi-party communication protocols. In contrast to protocols that are typically studied with session types, they are often designed to cope with system failures. An essential behavioural property is (successful) termination, despite failures, but it is often elaborate to prove for distributed algorithms.We extend multi-party session types (and multi-party session types with nested sessions) with optional blocks that cover a limited class of link failures. This allows us to automatically derive termination of distributed algorithms that come within these limits. To illustrate our approach, we prove termination for an implementation of the "rotating coordinator" Consensus algorithm. This paper is an extended version of Adameit et al. [2017].G n likewise for sequential composition. We naturally adapt these notations to local types and processes that are introduced later.Remember that global types specify a global point of view of the communication structure, whereas the pseudo code of Example 1.1 provides the local view for participant i containing also the data flow. Accordingly we obtain a global type for Example 1.1 by abstracting partly from the values; concentrating on the communications.Let v i,j be the value of participant i of Example 1.1 after round j such that v i,i := v i,i−1 (the coordinator does not update its value) and assume a vector (v 1,0 , . . . , v n,0 ) of initial values. Here only the initial values v i,0 are actually values, the remaining v i,j are variables that are instantiated with values during runtime. Then, in Example 2.3 (Global Type for Rotating Coordinators).the index i is used to specify the number of the current round, while j iterates over potential communication partners in round i. From a global point of view, there are n rounds such that each participant is exactly once the coordinator p i and transmits its value to all other participants p j using an unreliable link. This global type abstracts in particular from Line 5 in Example 1.1, since it does not specify that or how the values of the receivers are updated. For simplicity we do not consider the Lines 1 and 7. Global Types with Optional Blocks and Sub-SessionsAs it is the case for our running example, many distributed algorithms are organised in rounds or use similar concepts of modularisation. We want to be able to directly mirror this modularity. To do so, we make use of the extension of multi-party session types with nested sessions of Demangeon and Honda [2012]. These authors introduce two additional primitives for global types | let P = λr 1 ; ỹ : S → new r2 ....