Leader election in rings of ambient processes

Towards a Unified Approach to Encodability and Separation Results for Process Calculi

“…In this framework, the way in which we prove a separation result between L 1 and L 2 is the following: Notice that the identification of S 1 and S 2 (point (b) above) is usually very simple: they are directly obtained from the constructs of L 1 that one believes not to be encodable in L 2 . This is different from [9,17,29,32,33] where, instead, a lot of efforts must be spent to define a programming scenario that can be properly implemented in the source language but not in the target one. Point (c) is the only part that requires some ingenuity (it can be easy or quite difficult): usually, it strongly relies on Property 2 (sometimes also on compositionality) to slightly modify S 2 in order to obtain the new process S 2 .…”

“…of synchronous vs asynchronous π-calculus [8] or of persistent fragments of the asynchronous π-calculus [7]. However, for separation results, the most widely accepted criterion is homomorphism of parallel composition [9,17,29,30,32,33]; indeed, translating a parallel process by introducing a coordinating context would reduce the degree of distribution and show that L 2 has not enough expressive power to simulate L 1 . This point of view has been, however, sometimes criticized and, indeed, there exist encodings that do not translate parallel composition homomorphically [4,6,26].…”

“…those in [9,29,32,33], in a more uniform and abstract setting. To this aim, however, we must leave the ideal framework presented in Section 2 and make it slightly more concrete; carrying out proofs at the abstract level is a challenging open problem.…”

A taxonomy of process calculi for distribution and mobility

“…A weakening is to require that the encoding is 'two-level' (in [45] this is called weak compositionality): P|Q C( P|Q ), where C(·) is some context and the second-level encoding function · is compositional (in the way defined above). Compositionality can also be strenghtened (see, e.g., [11,44,47,48]), by imposing that the parallel operator is translated homomorphically: P|Q P | Q . All these formulations have their own merits and can be exploited in practice.…”

On the Relative Expressive Power of Ambient-Based Calculi

“…The encoding respects all our criteria but the target language is still another variant of the languages we have presented. Second, [17,18] are inspired by Palamidessi's work on electoral systems [15], where separation results are formulated according to the possibility/impossibility of electing a leader in a symmetric system (i.e. a set of parallel processes programmed in the same way, modulo renamings).…”