Randomization Adaptive Self-Stabilization

TL;DR

This paper introduces a scheme to modify self-stabilizing algorithms so they only use randomization during convergence, significantly reducing the randomness needed while maintaining effectiveness.

Contribution

The authors propose a novel scheme that transforms existing self-stabilizing algorithms to use bounded random bits, applicable when local predicates imply global consistency.

Findings

Applied scheme to token circulation algorithm demonstrating effectiveness.

Created the first constant-time Byzantine self-stabilizing clock synchronization with bounded randomness.

Showed reduction of random bits from infinite to bounded in self-stabilizing algorithms.

Abstract

We present a scheme to convert self-stabilizing algorithms that use randomization during and following convergence to self-stabilizing algorithms that use randomization only during convergence. We thus reduce the number of random bits from an infinite number to a bounded number. The scheme is applicable to the cases in which there exits a local predicate for each node, such that global consistency is implied by the union of the local predicates. We demonstrate our scheme over the token circulation algorithm of Herman and the recent constant time Byzantine self-stabilizing clock synchronization algorithm by Ben-Or, Dolev and Hoch. The application of our scheme results in the first constant time Byzantine self-stabilizing clock synchronization algorithm that uses a bounded number of random bits.