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arXiv · 2207.02045

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

Pablo F. Castro·Pedro D'Argenio·Luciano Putruele·Ramiro Demasi
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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.

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Pablo F. Castro, Pedro D'Argenio, Luciano Putruele, Ramiro Demasi. 2022-07-05. A Stochastic Game Approach to Masking Fault-Tolerance: Bisimulation and Quantification. https://arxiv.org/abs/2207.02045

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