Formal Probabilistic Analysis of Stuck-at Faults in Reconfigurable Memory Arrays
IFM '09 Proceedings of the 7th International Conference on Integrated Formal Methods
Probabilistic Analysis of Wireless Systems Using Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
Error Analysis and Verification of an IEEE 802.11 OFDM Modem using Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
Formal Reasoning about Expectation Properties for Continuous Random Variables
FM '09 Proceedings of the 2nd World Congress on Formal Methods
Formal lifetime reliability analysis using continuous random variables
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
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
Formal analysis of a scheduling algorithm for wireless sensor networks
ICFEM'11 Proceedings of the 13th international conference on Formal methods and software engineering
Formal reasoning about classified markov chains in HOL
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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Probabilistic analysis is a tool of fundamental importance to virtually all scientists and engineers as they often have to deal with systems that exhibit random or unpredictable elements. Traditionally, computer simulation techniques are used to perform probabilistic analysis. However, they provide less accurate results and cannot handle large-scale problems due to their enormous computer processing time requirements. To overcome these limitations, this thesis proposes to perform probabilistic analysis by formally specifying the behavior of random systems in higher-order logic and use these models for verifying the intended probabilistic and statistical properties in a computer based theorem prover. The analysis carried out in this way is free from any approximation or precision issues due to the mathematical nature of the models and the inherent soundness of the theorem proving approach. The thesis mainly targets the two most essential components for this task, i.e., the higher-order-logic formalization of random variables and the ability to formally verify the probabilistic and statistical properties of these random variables within a theorem prover. We present a framework that can be used to formalize and verify any continuous random variable for which the inverse of the cumulative distribution function can be expressed in a closed mathematical form. Similarly, we provide a formalization infrastructure that allows us to formally reason about statistical properties, such as mean, variance and tail distribution bounds, for discrete random variables. In order to in illustrate the practical effectiveness of the proposed approach, we consider the probabilistic analysis of three examples: the Coupon Collector's problem, the roundoff error in a digital processor and the Stop-and-Wait protocol. All the above mentioned work is conducted using the HOL theorem prover.