Parameter synthesis for Markov models: covering the parameter space

Author:

Junges Sebastian,Ábrahám Erika,Hensel Christian,Jansen NilsORCID,Katoen Joost-Pieter,Quatmann Tim,Volk Matthias

Abstract

AbstractMarkov chain analysis is a key technique in formal verification. A practical obstacle is that all probabilities in Markov models need to be known. However, system quantities such as failure rates or packet loss ratios, etc. are often not—or only partially—known. This motivates considering parametric models with transitions labeled with functions over parameters. Whereas traditional Markov chain analysis relies on a single, fixed set of probabilities, analysing parametric Markov models focuses on synthesising parameter values that establish a given safety or performance specification $$\varphi $$ φ . Examples are: what component failure rates ensure the probability of a system breakdown to be below 0.00000001?, or which failure rates maximise the performance, for instance the throughput, of the system? This paper presents various analysis algorithms for parametric discrete-time Markov chains and Markov decision processes. We focus on three problems: (a) do all parameter values within a given region satisfy $$\varphi $$ φ ?, (b) which regions satisfy $$\varphi $$ φ and which ones do not?, and (c) an approximate version of (b) focusing on covering a large fraction of all possible parameter values. We give a detailed account of the various algorithms, present a software tool realising these techniques, and report on an extensive experimental evaluation on benchmarks that span a wide range of applications.

Funder

Ruhr-Universität Bochum

Publisher

Springer Science and Business Media LLC

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Multifidelity Sim-to-Real Pipeline for Verifiable and Compositional Reinforcement Learning;2024 IEEE International Conference on Robotics and Automation (ICRA);2024-05-13

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