Mechanizing programming logics in higher order logic
Current trends in hardware verification and automated theorem proving
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
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Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
A probabilistic language based upon sampling functions
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Probabilistic guarded commands mechanized in HOL
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
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IBAL: a probabilistic rational programming language
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On the accuracy of statistical procedures in Microsoft Excel 2003
Computational Statistics & Data Analysis
Quantitative temporal logic mechanized in HOL
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CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Using Theorem Proving to Verify Expectation and Variance for Discrete Random Variables
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Verification of expectation properties for discrete random variables in HOL
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
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Traditionally, computer simulation techniques are used to perform probabilistic analysis. However, they provide inaccurate results and cannot handle large-scale problems due to their enormous CPU time requirements. To overcome these limitations, we propose to complement simulation based tools with higher-order-logic theorem proving so that an integrated approach can provide exact results for the critical sections of the analysis in the most efficient manner. In this paper, we illustrate the practical effectiveness of our idea by verifying numerous probabilistic properties associated with random variables in the HOL theorem prover. Our verification approach revolves around the fact that any probabilistic property associated with a random variable can be verified using the classical Cumulative Distribution Function (CDF) properties, if the CDF relation of that random variable is known. For illustration purposes, we also present the verification of a couple of probabilistic properties, which cannot be evaluated precisely by the existing simulation techniques, associated with the Continuous Uniform random variable in HOL.