A Calculus of Self-stabilising Computational Fields

Computational fields are spatially distributed data structures created by diffusion/aggregation processes, designed to adapt their shape to the topology of the underlying (mobile) network and to the events occurring in it: they have been proposed in a thread of recent works addressing self-organisation mechanisms for system coordination in scenarios including pervasive computing, sensor networks, and mobile robots. A key challenge for these systems is to assure behavioural correctness, namely, correspondence of micro-level specification (computational field specification) with macro-level behaviour (resulting global spatial pattern). Accordingly, in this paper we investigate the propagation process of computational fields, especially when composed one another to achieve complex spatial structures. We present a tiny, expressive, and type-sound calculus of computational fields, enjoying self-stabilisation, i.e., the ability of computational fields to react to changes in the environment finding a new stable state in finite time.