Type-based Self-stabilisation for Computational Fields

TL;DR

This paper introduces a type-based calculus for computational fields in large-scale network systems, ensuring their self-stabilisation and predictable global behaviour despite environmental changes.

Contribution

It presents a novel, type-sound calculus and conditions for self-stabilisation, enabling reliable and predictable behaviour in complex distributed systems.

Findings

Defined sufficient conditions for self-stabilisation.

Developed a type-based checking procedure for correctness.

Ensured finite-time convergence to stable states.

Abstract

Emerging network scenarios require the development of solid large-scale situated systems. Unfortunately, the diffusion/aggregation computational processes therein often introduce a source of complexity that hampers predictability of the overall system behaviour. Computational fields have been introduced to help engineering such systems: they are spatially distributed data structures designed to adapt their shape to the topology of the underlying (mobile) network and to the events occurring in it, with notable applications to pervasive computing, sensor networks, and mobile robots. To assure behavioural correctness, namely, correspondence of micro-level specification (single device behaviour) with macro-level behaviour (resulting global spatial pattern), we investigate the issue of self-stabilisation for computational fields. We present a tiny, expressive, and type-sound calculus of computational fields, and define sufficient conditions for self-stabilisation, defined as the ability to react to changes in the environment finding a new stable state in finite time. A type-based approach is used to provide a correct checking procedure for self-stabilisation.