Probability and statistics with reliability, queuing and computer science applications
Probability and statistics with reliability, queuing and computer science applications
VESTA: A Statistical Model-checker and Analyzer for Probabilistic Systems
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Formal probabilistic analysis using theorem proving
Formal probabilistic analysis using theorem proving
Formalization of finite-state discrete-time Markov chains in HOL
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
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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Classified Markov chains have been extensively applied to model and analyze various stochastic systems in many engineering and scientific domains. Traditionally, the analysis of these systems has been conducted using computer simulations and, more recently, also probabilistic model-checking. However, these methods either cannot guarantee accurate analysis or are not scalable due to the unacceptable computation times. As an alternative approach, this paper proposes to reason about classified Markov chains using HOL theorem proving. We provide a formalization of classified discrete-time Markov chains with finite state space in higher-order logic and the formal verification of some of their widely used properties. To illustrate the usefulness of the proposed approach, we present the formal analysis of a generic LRU (least recently used) stack model.