What Is a ‘Good’ Encoding of Guarded Choice?

The pi-calculus with synchronous output and mixed-guarded choices is strictly more expressive than the pi-calculus with asynchronous output and no choice. As a corollary, Palamidessi recently proved that there is no fully compositional encodingfrom the former into the latter that preserves divergence-freedom and symmetries. This paper shows that there are nevertheless `good' encodings between these calculi.In detail, we present a series of encodings for languages with (1) input-guarded choice, (2) both input- and output-guarded choice, and (3) mixed-guarded choice, and investigate them with respect to compositionality and divergence-freedom. The firstand second encoding satisfy all of the above criteria, but various `good' candidates for the third encoding - inspired by an existing distributed implementation - invalidate one or the other criterion. While essentially confirming Palamidessi's result, our studysuggests that the combination of strong compositionality and divergence-freedom is too strong for more practical purposes

What is a ‘Good’ Encoding of Guarded Choice?

The pi-calculus with synchronous output and mixed-guarded choices is strictly more expressive than the pi-calculus with asynchronous output and no choice. This result was recently proved by Palamidessi and, as a corollary, she showed that there is no fully compositional encoding from the former into the latter that preserves divergence-freedom and symmetries. This paper argues that there are nevertheless `good' encodings between these calculi. In detail, we present a series of encodings for languages with (1) input-guarded choice, (2) both input- and output-guarded choice, and (3) mixed-guarded choice, and investigate them with respect to compositionality and divergence-freedom. The first and second encoding satisfy all of the above criteria, but various `good' candidates for the third encoding - inspired by an existing distributed implementation - invalidate one or the other criterion. While essentially confirming Palamidessi's result, our study suggests that the combination of strong compositionality and divergence-freedom is too strong for more practical purposes

A criterion for separating process calculi

We introduce a new criterion, replacement freeness, to discern the relative expressiveness of process calculi. Intuitively, a calculus is strongly replacement free if replacing, within an enclosing context, a process that cannot perform any visible action by an arbitrary process never inhibits the capability of the resulting process to perform a visible action. We prove that there exists no compositional and interaction sensitive encoding of a not strongly replacement free calculus into any strongly replacement free one. We then define a weaker version of replacement freeness, by only considering replacement of closed processes, and prove that, if we additionally require the encoding to preserve name independence, it is not even possible to encode a non replacement free calculus into a weakly replacement free one. As a consequence of our encodability results, we get that many calculi equipped with priority are not replacement free and hence are not encodable into mainstream calculi like CCS and pi-calculus, that instead are strongly replacement free. We also prove that variants of pi-calculus with match among names, pattern matching or polyadic synchronization are only weakly replacement free, hence they are separated both from process calculi with priority and from mainstream calculi.Comment: In Proceedings EXPRESS'10, arXiv:1011.601

Analysing and Comparing Encodability Criteria

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

Breaking Symmetries

A well-known result by Palamidessi tells us that {\pi}mix (the {\pi}-calculus with mixed choice) is more expressive than {\pi}sep (its subset with only separate choice). The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla of- fered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of "incestual" processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (ini- tial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result-based on a proper formalization of what it means to break symmetries-without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reason- able encoding from {\pi}mix into {\pi}sep . We indicate how the respective proofs can be adapted and exhibit the consequences of varying notions of uniformity and reasonableness. In each case, the ability to break initial symmetries turns out to be essential

Musings on Encodings and Expressiveness

This paper proposes a definition of what it means for one system description language to encode another one, thereby enabling an ordering of system description languages with respect to expressive power. I compare the proposed definition with other definitions of encoding and expressiveness found in the literature, and illustrate it on a case study: comparing the expressive power of CCS and CSP.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244

Explicit fairness in testing semantics

In this paper we investigate fair computations in the pi-calculus. Following Costa and Stirling's approach for CCS-like languages, we consider a method to label process actions in order to filter out unfair computations. We contrast the existing fair-testing notion with those that naturally arise by imposing weak and strong fairness. This comparison provides insight about the expressiveness of the various `fair' testing semantics and about their discriminating power.Comment: 27 pages, 1 figure, appeared in LMC

Expressiveness of Process Algebras

AbstractWe examine ways to measure expressiveness of process algebras, and recapitulate and compare some related results from the literature