The dining cryptographers problem: unconditional sender and recipient untraceability
Journal of Cryptology
Mechanizing programming logics in higher order logic
Current trends in hardware verification and automated theorem proving
Elements of information theory
Elements of information theory
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Crowds: anonymity for Web transactions
ACM Transactions on Information and System Security (TISSEC)
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
VESTA: A Statistical Model-checker and Analyzer for Probabilistic Systems
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Topology in PVS: continuous mathematics with applications
Proceedings of the second workshop on Automated formal methods
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Performance Analysis and Functional Verification of the Stop-and-Wait Protocol in HOL
Journal of Automated Reasoning
On the Foundations of Quantitative Information Flow
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Handbook of Practical Logic and Automated Reasoning
Handbook of Practical Logic and Automated Reasoning
Formal Reasoning about Expectation Properties for Continuous Random Variables
FM '09 Proceedings of the 2nd World Congress on Formal Methods
Quantitative Analysis With the Probabilistic Model Checker PRISM
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Formal Reliability Analysis Using Theorem Proving
IEEE Transactions on Computers
On the formalization of the lebesgue integration theory in HOL
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
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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.