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Formal Reasoning About Finite-State Discrete-Time Markov Chains in HOL

Title:

Formal Reasoning About Finite-State Discrete-Time Markov Chains in HOL

Liu, Liya, Hasan, Osman and Tahar, Sofiène (2013) Formal Reasoning About Finite-State Discrete-Time Markov Chains in HOL. Journal of Computer Science and Technology, 28 (2). pp. 217-231. ISSN 1000-9000

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Official URL: http://dx.doi.org/10.1007/s11390-013-1324-6

Abstract

Markov chains are extensively used in modeling different aspects of engineering and scientific systems, such as performance of algorithms and reliability of systems. Different techniques have been developed for analyzing Markovian models, for example, Markov Chain Monte Carlo based simulation, Markov Analyzer, and more recently probabilistic model-checking. However, these techniques either do not guarantee accurate analysis or are not scalable. Higher-order-logic theorem proving is a formal method that has the ability to overcome the above mentioned limitations. However, it is not mature enough to handle all sorts of Markovian models. In this paper, we propose a formalization of Discrete-Time Markov Chain (DTMC) that facilitates formal reasoning about time-homogeneous finite-state discrete-time Markov chain. In particular, we provide a formal verification on some of its important properties, such as joint probabilities, Chapman-Kolmogorov equation, reversibility property, using higher-order logic. To demonstrate the usefulness of our work, we analyze two applications: a simplified binary communication channel and the Automatic Mail Quality Measurement protocol.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Refereed:Yes
Authors:Liu, Liya and Hasan, Osman and Tahar, Sofiène
Journal or Publication:Journal of Computer Science and Technology
Date:2013
Digital Object Identifier (DOI):10.1007/s11390-013-1324-6
Keywords:discrete-time Markov chain; higher-order logic; probability theory; theorem prover
ID Code:977339
Deposited By: DANIELLE DENNIE
Deposited On:11 Jun 2013 19:56
Last Modified:18 Jan 2018 17:44

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