Name
Title | ||
|---|---|---|
Formalization of Measure Theory and Lebesgue Integration for Probabilistic Analysis in HOL |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1145/2406336.2406349 | ACM Trans. Embedded Comput. Syst. |
Keywords | Field | DocType |
exhibit probabilistic behavior,measure theory,generalized methodology,air traffic control,hol theorem prover,probabilistic system,basic concept,probabilistic analysis,classical result,lebesgue integration,theorem prover,theorem proving,information theory | Information theory,HOL,Dependability,Computer science,Measure (mathematics),Parallel computing,Automated theorem proving,Theoretical computer science,Probabilistic analysis of algorithms,Probabilistic logic,Lebesgue integration | Journal |
Volume | Issue | ISSN |
12 | 1 | 1539-9087 |
Citations | PageRank | References |
1 | 0.34 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tarek Mhamdi | 1 | 61 | 4.15 |
| Osman Hasan | 2 | 401 | 60.79 |
| Sofiène Tahar | 3 | 915 | 110.41 |