Shadow/Puppet Synthesis: A Stepwise Method for the Design of Self-Stabilization

Abstract

This paper presents a novel two-step method for automated design of self-stabilization. The first step enables the specification of legitimate states and an intuitive (but imprecise) specification of the desired functional behaviors in the set of legitimate states (hence the term “shadow”). After creating the shadow specifications, we systematically introduce the main variables and the topology of the desired self-stabilizing system. Subsequently, we devise a parallel and complete backtracking search towards finding a self-stabilizing solution that implements a precise version of the shadow behaviors, and guarantees recovery to legitimate states from any state. To the best of our knowledge, the shadow/puppet synthesis is the first sound and complete method that exploits parallelism and randomization along with the expansion of the state space towards generating self-stabilizing systems that cannot be synthesized with existing methods. We have validated the proposed method by creating both a sequential and a parallel implementation in the context of a software tool, called Protocon. Moreover, we have used Protocon to automatically design three new self-stabilizing protocols that we conjecture to require the minimal number of states per process to achieve stabilization (when processes are deterministic): 2-state maximal matching on bidirectional rings, 5-state token passing on unidirectional rings, and 3-state token passing on bidirectional chains.