A Fully Abstract Encoding of the π-Calculus with Data Terms

Abstract

Abstract. The π-calculus with data terms (πT) extends the pure π-calculus by data constructors and destructors and allows data to be transmitted between agents. It has long been known how to encode such data types in π, but until now it has been open how to make the encoding fully abstract, meaning that two encodings (in π) are semantically equivalent precisely when the original πT agents are semantically equivalent. We present a new type of encoding and prove it to be fully abstract with respect to may-testing equivalence. To our knowledge this is the first result of its kind, for any calculus enriched with data terms. It has particular importance when representing security properties since attackers can be regarded as may-test observers. Full abstraction proves that it does not matter whether such observers are formulated in π or πT, both are equally expressive in this respect. The technical new idea consists of achieving full abstraction by encoding data as table entries rather than active processes, and using a firewalled central integrity manager to ensure data security.

A taxonomy of process calculi for distribution and mobility

“…the top-level encoding is defined by a top-level context (viz., l : ) and by a compositional process translation (i.e., the identity in this case). Of course, this encodability result is not as strong as the other ones in this paper, but it is similar to other encodings in the literature (e.g., [4,5,9]). …”

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

“…For example, it may happen to have a 'two-level' encoding [4,6] where · is a translation that satisfies Properties 2-5 and is such that P C F(P) [ P ], where · is a compositional translation (this property is called weak compositionality in [31]). The proof-techniques presented in Sections 3.2 and 3.3 can be readily adapted to this enhanced notion of encoding, whereas the proof-technique of Section 3.1 cannot (recall that there we had to work with homomorphic translations of parallel composition).…”

“…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].…”

The Attributed Pi-Calculus with Priorities

“…The π-calculus with polyadic synchronization was first proposed in [17] but could be extended by more general data terms as in [30] without particular difficulties. An extended π-calculus with polyadic synchronization, data terms, and explicit substitutions motivated by security applications was proposed in [31].…”