A Stochastic Game Approach to Masking Fault-Tolerance: Bisimulation and Quantification

TL;DR

This paper introduces a formal framework for assessing masking fault-tolerance in probabilistic systems using bisimulation and game theory, providing polynomial-time decision procedures and a quantifiable fault-tolerance metric.

Contribution

It develops a novel probabilistic bisimulation-based notion of masking fault-tolerance, with a symbolic polynomial-time decision method and a metric for almost-sure failing systems.

Findings

Polynomial-time decision procedure for masking simulation

A new metric quantifying fault-tolerance levels

Prototype implementation demonstrating practical applicability

Abstract

We introduce a formal notion of masking fault-tolerance between probabilistic transition systems based on a variant of probabilistic bisimulation (named masking simulation). We also provide the corresponding probabilistic game characterization. Even though these games could be infinite, we propose a symbolic way of representing them, such that it can be decided in polynomial time if there is a masking simulation between two probabilistic transition systems. We use this notion of masking to quantify the level of masking fault-tolerance exhibited by almost-sure failing systems, i.e., those systems that eventually fail with probability 1. The level of masking fault-tolerance of almost-sure failing systems can be calculated by solving a collection of functional equations. We produce this metric in a setting in which the minimizing player behaves in a strong fair way (mimicking the idea of fair environments), and limit our study to memoryless strategies due to the infinite nature of the game. We implemented these ideas in a prototype tool, and performed an experimental evaluation.