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Formalization of Measure Theory and Lebesgue Integration for Probabilistic Analysis in HOL


Formalization of Measure Theory and Lebesgue Integration for Probabilistic Analysis in HOL

Mhamdi, Tarek, Hasan, Osman and Tahar, Sofiène (2013) Formalization of Measure Theory and Lebesgue Integration for Probabilistic Analysis in HOL. ACM Transactions on Embedded Computing Systems, 12 (1). pp. 1-23. ISSN 15399087

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Official URL: http://dx.doi.org/10.1145/2406336.2406349


Dynamic systems that exhibit probabilistic behavior represent a large class of man-made systems such as communication networks, air traffic control, and other mission-critical systems. Evaluation of quantitative issues like performance and dependability of these systems is of paramount importance. In this paper, we propose a generalized methodology to formally reason about probabilistic systems within a theorem prover. We present a formalization of measure theory in the HOL theorem prover and use it to formalize basic concepts from the theory of probability. We also use the Lebesgue integration to formalize statistical properties of random variables. To illustrate the practical effectiveness of our methodology, we formally prove classical results from the theories of probability and information and use them in a data compression application in HOL.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Authors:Mhamdi, Tarek and Hasan, Osman and Tahar, Sofiène
Journal or Publication:ACM Transactions on Embedded Computing Systems
Date:January 2013
Digital Object Identifier (DOI):10.1145/2406336.2406349
Keywords:information theory; lebesgue integration; measure theory; probabilistic systems; proof theory; reliability; statistical properties; theorem proving; verification;
ID Code:977357
Deposited By: Danielle Dennie
Deposited On:14 Jun 2013 13:06
Last Modified:18 Jan 2018 17:44


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