Iain Phillips

On the computational strength of pure ambient calculi

Cardelli and Gordons calculus of Mobile Ambients has attracted widespread interest as a model of mobile computation. The standard calculus is quite rich, with a variety of operators, together with capabilities for entering, leaving and dissolving ambients. The question arises of what is a minimal Turing-complete set of constructs. Previous work has established that Turing completeness can be achieved without using communication or restriction. We show that it can be achieved merely using movement capabilities (and not dissolution). We also show that certain smaller sets of constructs are either terminating or have decidable termination.

A Reversible Process Calculus and the Modelling of the ERK Signalling Pathway

We introduce a reversible process calculus with a new feature of execution control that allows us to change the direction and pattern of computation. This feature allows us to model a variety of modes of reverse computation, ranging from strict backtracking to reversing which respects causal ordering of events, and even reversing which violates causal ordering. The SOS rules that define the operators of the new calculus employ communication keys to handle communication correctly and key identifiers to control execution.

On Reduction Semantics for the Push and Pull Ambitent Calculus

Honda and Yoshida showed how to obtain a meaningful equivalence on processes in the asynchronous π-calculus using equational theories identifying insensitive processes. We apply their approach to a dialect of Cardelli and Gordon’s Mobile Ambients. The version we propose here is the Push and Pull Ambient Calculus, where the operational semantics is no longer defined in terms of ambients entering and exiting other ambients, but in terms of being pulled and being pushed away by another ambient. Like the standard ambient calculus, this dialect has the computational power of the asynchronous π-calculus. We contend that the new calculus allows a better modelling of certain security issues.

Ordered SOS process languages for branching and Eager bisimulation

We present a general and uniform method for defining structural operational semantics (SOS) of process operators by traditional Plotkin-style transition rules equipped with orderings. This new feature allows one to control the order of application of rules when deriving transitions of process terms. Our method is powerful enough to deal with rules with negative premises and copying. We show that rules with orderings, called ordered SOS rules, have the same expressive power as GSOS rules. We identify several classes of process languages with operators defined by rules with and without orderings in the setting with silent actions and divergence. We prove that branching bisimulation and eager bisimulation relations are preserved by all operators in process languages in the relevant classes.

Reversibility and Models for Concurrency

There is a growing interest in models of reversible computation driven by exciting application areas such as bio-systems and quantum computing. Reversible process algebras RCCS [Danos, V. and J. Krivine, Reversible communicating systems, in: P. Gardner and N. Yoshida, editors, Proceedings of the 15th International Conference on Concurrency Theory CONCUR 2004, LNCS 3170 (2004), pp. 292-307] and CCSK [Phillips, I.C.C. and I. Ulidowski, Reversing algebraic process calculi, in: Proceedings of 9th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2006, LNCS 3921 (2006), pp. 246-260. Extended version accepted by Journal of Logic and Algebraic Programming] were developed and general techniques for reversing other process operators were proposed. The paper shows that the notion of reversibility can bridge the gap between some interleaving models and non-interleaving models of concurrency, and makes them interchangeable. We prove that transition systems associated with reversible process algebras are equivalent as models to labelled prime event structures. Furthermore, we show that forward-reverse bisimulation corresponds to hereditary history-preserving bisimulation in the setting with no auto-concurrency and no auto-causation.

CCS with priority guards

Abstract It has long been recognised that standard process algebra has difficulty dealing with actions of different priority, such as for instance an interrupt action of high priority. Various solutions have been proposed. We introduce a new approach, involving the addition of “priority guards” to Milner’s process calculus CCS. In our approach, priority is unstratified , meaning that actions are not assigned fixed levels, so that the same action can have different priority depending where it appears in a program. Unlike in other unstratified accounts of priority in CCS (such as that of Camilleri and Winskel), we treat inputs and outputs symmetrically. We introduce the new calculus, give examples, develop its theory (including bisimulation and equational laws), and compare it with existing approaches. We use leader election problems to show that priority adds expressiveness to both CCS and the π -calculus.

Electoral Systems in Ambient Calculi

This paper compares the expressiveness of ambient calculi against different dialects of the pi-calculus. Cardelli and Gordon encoded the asynchronous pi-calculus into their calculus of Mobile Ambients (MA). Zimmer has shown that the synchronous pi-calculus without choice can be encoded in pure (no communication) Safe Ambients. We show that pure MA without restriction has symmetric electoral systems, that is, it is possible to solve the problem of electing a leader in a symmetric network. By the work of Palamidessi, this implies that pure MA without restriction is not encodable (under certain conditions) in the pi-calculus with separate choice. We adapt the work of Carbone and Maffeis to show that pure MA cannot be encoded (under certain other conditions) into the pi-calculus with mixed choice (but without matching).

Tutorial on separation results in process calculi via leader election problems

We compare the expressive power of process calculi by studying the problem of electing a leader in a symmetric network of processes. We consider the @p-calculus with mixed choice, separate choice and internal mobility, value-passing CCS and Mobile Ambients, together with other ambient calculi (Safe Ambients, the Push and Pull Ambient Calculus and Boxed Ambients). We provide a unified approach for all these calculi using reduction semantics.

Reversing algebraic process calculi

Reversible computation has a growing number of promising application areas such as the modelling of biochemical systems, program debugging and testing, and even programming languages for quantum computing. We formulate a procedure for converting operators of standard algebraic process calculi such as CCS, ACP and CSP into reversible operators, while preserving their operational semantics.

Leader election in rings of ambient processes

Palamidessi has shown that the π-calculus with mixed choice is powerful enough to solve the leader election problem on a symmetric ring of processes. We show that this is also possible in the calculus of Mobile Ambients (MA), without using communication or restriction. Following Palamidessis methods, we deduce that there is no encoding satisfying certain conditions from MA into CCS. We also show that the calculus of Boxed Ambients is more expressive than its communication-free fragment.