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Introduction to HOL: a theorem proving environment for higher order logic
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Introduction to Monte Carlo methods
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QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Formalization of the Standard Uniform random variable
Theoretical Computer Science
Principles of Model Checking (Representation and Mind Series)
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Formalization of Continuous Probability Distributions
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
Journal of Automated Reasoning
Performance Analysis and Functional Verification of the Stop-and-Wait Protocol in HOL
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Handbook of Practical Logic and Automated Reasoning
Handbook of Practical Logic and Automated Reasoning
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FM '09 Proceedings of the 2nd World Congress on Formal Methods
Formal Reasoning about Expectation Properties for Continuous Random Variables
FM '09 Proceedings of the 2nd World Congress on Formal Methods
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IFM'07 Proceedings of the 6th international conference on Integrated formal methods
Formal Reliability Analysis Using Theorem Proving
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ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Theorem Proving with the Real Numbers
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ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part III
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Traditionally, simulation is used to perform probabilistic analysis. However, it provides less accurate results and cannot handle large-scale problems due to the enormous CPU time requirements. Recently, a significant amount of formalization has been done in higher-order logic that allows us to conduct precise probabilistic analysis using theorem proving and thus overcome the limitations of the simulation. Some major contributions include the formalization of both discrete and continuous random variables and the verification of some of their corresponding probabilistic and statistical properties. This paper describes the infrastructures behind these capabilities and their utilization to conduct the probabilistic analysis of real-world systems.