Causality and replication in concurrent processes

The replication operator was introduced by Milner for obtaining a simplified description of recursive processes. The standard interleaving semantics denotes the replication of a process P, written !P, a shorthand for its unbound parallel composition, operationally equivalent to the process P | P | …, with P repeated as many times as needed. Albeit the replication mechanism has become increasingly popular, investigations on its causal semantics has been scarce. In fact, the correspondence between replication and unbound parallelism makes it difficult to recover basic properties usually associated with these semantics, such as the so-called concurrency diamond. In this paper we consider the interleaving semantics for the operator proposed by Sangiorgi and Walker, and we show how to refine it in order to capture causality. Furthermore, we prove it coincident with the standard causal semantics for recursive process studied in the literature, for processes defined by means of constant invocations

Causal computational complexity of distributed processes

This article studies the complexity of π-calculus processes with respect to the quantity of transitions caused by an incoming message. First, we propose a typing system for integrating Bellantoni and Cook's characterisation of polytime computable functions into Deng and Sangiorgi's typing system for termination. We then define computational complexity of distributed messages based on Degano and Priami's causal semantics, which identifies the dependency between interleaved transitions. Next, we apply a necessary syntactic flow analysis to typable processes to ensure a computational bound on the number of distributed messages. We prove that our analysis is decidable; sound in the sense that it guarantees that the total number of messages causally dependent of an input request received from the outside is bounded by a polynomial of the content of this request; and complete, meaning that each polynomial recursive function can be computed by a typable process

Causality and Replication in Concurrent Processes

The replication operator was introduced by Milner for obtaining a simplified description of recursive processes. The standard interleaving semantics denotes the replication of a process P, written IP, a shorthand for its unbound parallel composition, operationally equivalent to the process P | P | . . . , with P repeated as many times as needed. Albeit the replication mechanism has become increasingly popular, investigations on its causal semantics has been scarce. In our work we consider the interleaving semantics for the operator proposed by Sangiorgi and Walker, and we show how to refine it in order to capture causality. Furthermore, we prove that a basic property usually associated to these semantics, the so-called concurrency diamond, does hold in our framework, and we sketch a correspondence between our proposal and the standard causal semantics for recursive process studied in the literature, for processes defined through constant invocations