Björn Victor

The fusion calculus: expressiveness and symmetry in mobile processes

We present the fusion calculus as a significant step towards a canonical calculus of concurrency. It simplifies and extends the /spl pi/-calculus. The fusion calculus contains the polyadic /spl pi/-calculus as a proper subcalculus and thus inherits all its expressive power. The gain is that fusion contains actions akin to updating a shared state, and a scoping construct for bounding their effects. Therefore it is easier to represent computational models such as concurrent constraints formalisms. It is also easy to represent the so called strong reduction strategies in the /spl lambda/-calculus, involving reduction under abstraction. In the /spl lambda/-calculus these tasks require elaborate encodings. Our results on the fusion calculus in this paper are the following. We give a structured operational semantics in the traditional style. The novelty lies in a new kind of action, fusion actions for emulating updates of a shared state. We prove that the calculus contains the /spl pi/-calculus as a subcalculus. We define and motivate the bisimulation equivalence and prove a simple characterization of its induced congruence, which is given two versions of a complete axiomatization for finite terms. The expressive power of the calculus is demonstrated by giving a straight-forward encoding of the strong lazy /spl lambda/-calculus, which admits reduction under /spl lambda/ abstraction.

The Mobility Workbench - A Tool for the pi-Calculus

In this paper we describe the first prototype version of the Mobility Workbench (MWB), an automated tool for manipulating and analyzing mobile concurrent systems (those with evolving connectivity s ...

Psi-calculi: Mobile Processes, Nominal Data, and Logic

A psi-calculus is an extension of the pi-calculus with nominal data types for data structures and for logical assertions representing facts about data. These can be transmitted between processes and their names can be statically scoped using the standard pi-calculus mechanism to allow for scope migrations. Other proposed extensions of the pi-calculus can be formulated as psi-calculi; examples include the applied pi-calculus, the spi-calculus, the fusion calculus, the concurrent constraint pi-calculus, and calculi with polyadic communication channels or pattern matching. Psi-calculi can be even more general, for example by allowing structured channels, higher-order formalisms such as the lambda calculus for data structures, and a predicate logic for assertions. Our labelled operational semantics and definition of bisimulation is straightforward, without a structural congruence. We establish minimal requirements on the nominal data and logic in order to prove general algebraic properties of psi-calculi. The proofs have been checked in the interactive proof checker Isabelle. We are the first to formulate a truly compositional labelled operational semantics for calculi of this calibre. Expressiveness and therefore modelling convenience significantly exceeds that of other formalisms, while the purity of the semantics is on par with the original pi-calculus.

Solos in concert

We present a calculus of mobile processes without prefix or summation, called the solos calculus. Using two different encodings, we show that the solos calculus can express both action prefix and guarded summation. One encoding gives a strong correspondence, but uses a match operator; the other yields a slightly weaker correspondence, but uses no additional operators. We also show that the expressive power of the solos calculus is still retained by the sub-calculus where actions carry at most two names. On the other hand, expressiveness is lost in the solos calculus without match and with actions carrying at most one name.

The update calculus

In the update calculus concurrent processes can perform update actions with side effects, and a scoping operator can be used to control the extent of the update. In this way it incorporates fundamental concepts both from imperative languages or concurrent constraints formalisms, and from functional formalisms such as the λ- and π-calculi. Structurally it is similar to but simpler than the π-calculus; it has only one binding operator and a symmetry between input and output. We define the structured operational semantics and the proper bisimulation equivalence and congruence, and give a complete axiomatization. The π-calculus turns out to be an asymmetric subcalculus.

On the Expressiveness of Linearity vs Persistence in the Asychronous Pi-Calculus

We present an expressiveness study of linearity and persistence of processes. We choose the pi-calculus, one of the main representatives of process calculi, as a framework to conduct our study. We consider four fragments of the pi-calculus. Each one singles out a natural source of linearity/persistence also present in other frameworks such as concurrent constraint programming (CCP), linear CCP, and several calculi for security. The study is presented by providing (or proving the non-existence of) encodings among the fragments, a processes-as-formulae interpretation and a reduction from, Minsky machines

Concurrent Constraints in the Fusion Calculus

We present exact algorithms with exponential running times for variants of n-element set cover problems, based on divide-and-conquer and on inclusion-exclusion characterisations. We show that the Exact Satisfiability problem of size 1 with m clauses can be solved in time 2(m)l(O(1)) and polynomial space. The same bounds hold for counting the number of solutions. As a special case, we can count the number of perfect matchings in an n-vertex graph in time 2(n)n(O(1)) and polynomial space. We also show how to count the number of perfect matchings in time O(1.732(n)) and exponential space. Using the same techniques we show how to compute Chromatic Number of an n-vertex graph in time O(2.4423(n)) and polynomial space, or time O(2.3236(n)) and exponential space. (Less)

Broadcast psi-calculi with an application to wireless protocols

Psi-calculi is a parametric framework for extensions of the pi-calculus, with arbitrary data structures and logical assertions for facts about data. In this paper we add primitives for broadcast communication in order to model wireless protocols. The additions preserve the purity of the psi-calculi semantics, and we formally prove the standard congruence and structural properties of bisimilarity. We demonstrate the expressive power of broadcast psi-calculi by modelling the wireless ad-hoc routing protocol LUNAR and verifying a basic reachability property.

The Tau-Laws of Fusion

We present complete axiomatizations of weak hypcrcongruence in the finite fragment of the fusion calculus, an extension and simplification of the π-calculus. We treat both the full fusion calculus and the subcalculus without mismatch operators. The axiomatizations are obtained from the laws for hyperequivalence and adding so called tau-laws. These are similar to the well known tau-laws for CCS and the π-calculus, but there is an interesting difference which highlights an aspect of the higher expressive power of the fusion calculus.

A fully abstract encoding of the π-calculus with data terms

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.