Synthesizing optimal bias in randomized self-stabilization.

Area of Science:

• Distributed computing
• Theoretical computer science
• Formal methods

Background:

• Randomization is crucial for self-stabilization in anonymous networks to overcome impossibility results.
• Optimal coin bias in self-stabilizing algorithms is not well understood, impacting expected convergence time.
• Existing methods lack automated techniques for determining optimal coin bias.

Purpose of the Study:

• To propose and evaluate a technique for automatically synthesizing the optimal coin bias in self-stabilizing algorithms.
• To minimize the expected convergence time of self-stabilizing protocols.
• To demonstrate the technique's applicability to Herman's token ring algorithm.

Main Methods:

• Parameter synthesis approach from probabilistic model checking.
• Iterative refinement of parameter regions for minimal convergence time.
• Over- and under-approximation techniques to bound the optimal parameter space.
• Analysis of algorithm variants and the impact of speed reducers.

Main Results:

• The developed technique successfully synthesizes optimal coin bias for self-stabilizing algorithms.
• For Herman's token ring algorithm, a fair coin is optimal for small rings.
• A biased coin is optimal for larger rings, with the bias growing with ring size.
• Speed reducers can improve the expected convergence time of Herman's protocol.

Conclusions:

• Automated synthesis of optimal coin bias is feasible and effective for self-stabilizing systems.
• The optimal coin bias depends on network size, challenging the assumption of fair coin usage.
• The proposed technique provides a systematic way to enhance the performance of randomized distributed algorithms.