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Probability as typicality
, 2006
"... The concept of typicality refers to properties holding for the “vast majority” of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measuretheoretical typicality would be the adequate viewpoint of the role of probability in classical statistical mechan ..."
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The concept of typicality refers to properties holding for the “vast majority” of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measuretheoretical typicality would be the adequate viewpoint of the role of probability in classical statistical mechanics, particularly in understanding the micro to macroscopic change of levels of description. Keywords: Statistical mechanics; Typicality; Probability.
Feedback Shift Register Sequences
"... Feedback Shift Register (FSR) sequences have been successfully implemented in many communication systems for their randomness properties and ease of implementation. These include ranging and navigation systems, spread spectrum communication systems, CDMA mobile communication systems, and crypto syst ..."
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Feedback Shift Register (FSR) sequences have been successfully implemented in many communication systems for their randomness properties and ease of implementation. These include ranging and navigation systems, spread spectrum communication systems, CDMA mobile communication systems, and crypto systems such as streamciphers. This article gives a brief overview of FSR sequences, both linear and nonlinear. Two conditions on the connection logic of FSRs for better output sequences are described, which are the branchless condition and the balanced logic condition. We use mostly the state transition diagram of an FSR to describe the property of its output sequences. For linear FSR sequences, we describe the relation between the connection polynomials and the structure of the cycle decomposition in the state diagram, and hence the periodicity of the output sequences. Various randomness properties of the maximal length linear FSR sequences, known as msequences, are described: balance, rundistribution, span, ideal autocorrelation, constantonthecoset, and cycleandadd properties. Two properties, the ideal autocorrelation function and the smallest linear complexity, of msequences are described in detail. Finally, a complete analysis of 4stage FSRs is provided.
THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume 9, Number 3/2008, pp. 000–000 RANDOM DEGREES OF UNBIASED BRANCHES
"... In our previous published research we discovered some very difficult to predict branches, called unbiased branches that have a “random ” dynamical behavior. We developed some improved state of the art branch predictors to predict successfully unbiased branches. Even these powerful predictors obtaine ..."
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In our previous published research we discovered some very difficult to predict branches, called unbiased branches that have a “random ” dynamical behavior. We developed some improved state of the art branch predictors to predict successfully unbiased branches. Even these powerful predictors obtained very modest average prediction accuracies on the unbiased branches while their global average prediction accuracies are high. These unbiased branches still restrict the ceiling of dynamic branch prediction and therefore accurately predicting unbiased branches remains an open problem. Starting from this technical challenge, we tried to understand in more depth what randomness is. Based on a hybrid mathematical and computer science approach we mainly developed some degrees of random associated to a branch in order to understand deeply what an unbiased branch is. These metrics are program’s Kolmogorov complexity, compression rate, discrete entropy and HMM prediction’s accuracy, that are useful for characterizing strings of symbols and particularly, our unbiased branches ’ behavior. All these random degree metrics could effectively help the computer architect to better understand branches ’ predictability, and also if the branch predictor should be improved related to the unbiased branches.