Results 1 
4 of
4
Probabilistic Analysis using Theorem Proving
"... Abstract. Traditionally, computer simulation techniques are used to perform probabilistic analysis. However, they provide less accurate results and cannot handle largescale problems due to their enormous CPU time requirements. Recently, a significant amount of formalization has been done in the HOL ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract. Traditionally, computer simulation techniques are used to perform probabilistic analysis. However, they provide less accurate results and cannot handle largescale problems due to their enormous CPU time requirements. Recently, a significant amount of formalization has been done in the HOL theorem prover that allows us to conduct precise probabilistic analysis using theorem proving and thus overcome the limitations of the simulation based probabilistic analysis approach. 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 presents a concise description of the infrastructures behind these capabilities and the utilization of these features to conduct the probabilistic analysis of realworld systems. For illustration purposes, the paper describes the theorem proving based probabilistic analysis of three examples, i.e., the roundoff error of a digital processor, the Coupon Collector’s problem and the StopandWait protocol. 1
Probabilistic Analysis of Wireless Systems using Theorem Proving
"... Probabilistic techniques play a major role in the design and analysis of wireless systems as they contain a significant amount of random or unpredictable components. Traditionally, computer simulation techniques are used to perform probabilistic analysis of wireless systems but they provide inaccura ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Probabilistic techniques play a major role in the design and analysis of wireless systems as they contain a significant amount of random or unpredictable components. Traditionally, computer simulation techniques are used to perform probabilistic analysis of wireless systems but they provide inaccurate results and usually require enormous amount of CPU time in order to attain reasonable estimates. To overcome these limitations, we propose to use a higherorderlogic theorem prover (HOL) for the analysis of wireless systems. The paper presents a concise description of the formal foundations required to conduct the analysis of a wireless system in a theorem prover, such as, the higherorderlogic modeling of random variables and the verification of their corresponding probabilistic and statistical properties in a theorem prover. In order to illustrate the utilization and effectiveness of the proposed idea for handling realworld wireless system analysis problems, we present an analysis of the automated repeat request (ARQ) mechanism at the logic link control (LLC) layer of the General Packet Radio Service (GPRS), which is a packet oriented mobile data service available to the users of Global System for Mobile Communications (GSM).
A Framework for Computer Proofs in Probability Theory for Use in Cryptography 1
"... Mathematical proofs are often complex and hard to verify by their readers. Consequently, the application of formal proof systems are a useful approach in the area of verification. We present a framework for computer proofs in probability theory. Therefore we describe formalized probability distribut ..."
Abstract
 Add to MetaCart
Mathematical proofs are often complex and hard to verify by their readers. Consequently, the application of formal proof systems are a useful approach in the area of verification. We present a framework for computer proofs in probability theory. Therefore we describe formalized probability distributions and fundamental lemmata concerning σalgebras, probability spaces and conditional probabilities. These are given in the formal language of the formal proof system Isabelle/HOL. Besides we describe an application of the presented formalized probability distributions and fundamental lemmata to cryptography. Our achievements are a step towards computer verification of cryptographic primitives. They describe a basis for computer verification in probability theory for interactive proof constructions within the formal proof system mentioned above. Computer verification can be applied to further problems in cryptographic research, if the corresponding basic mathematical
Formal Reasoning about Expectation Properties for Continuous Random Variables
"... Abstract. Expectation (average) properties of continuous random variables are widely used to judge performance characteristics in engineering and physical sciences. This paper presents an infrastructure that can be used to formally reason about expectation properties of most of the continuous random ..."
Abstract
 Add to MetaCart
Abstract. Expectation (average) properties of continuous random variables are widely used to judge performance characteristics in engineering and physical sciences. This paper presents an infrastructure that can be used to formally reason about expectation properties of most of the continuous random variables in a theorem prover. Starting from the relatively complex higherorderlogic definition of expectation, based on Lebesgue integration, we formally verify key expectation properties that allow us to reason about expectation of a continuous random variable in terms of simple arithmetic operations. In order to illustrate the practical effectiveness and utilization of our approach, we also present the formal verification of expectation properties of the commonly used continuous random variables: Uniform, Triangular and Exponential. 1