Prioritizing MCDC test cases by spectral analysis of Boolean functions

Test case prioritization aims at scheduling test cases in an order that improves some performance goal. One performance goal is a measure of how quickly faults are detected. Such prioritization can be performed by exploiting the Fault Exposing Potential (FEP) parameters associated to the test cases. FEP is usually approximated by mutation analysis under certain fault assumptions. Although this technique is effective, it could be relatively expensive compared to the other prioritization techniques. This study proposes a cost-effective FEP approximation for prioritizing Modified Condition Decision Coverage (MCDC) test cases. A strict negative correlation between the FEP of a MCDC test case and the influence value of the associated input condition allows to order the test cases easily without the need of an extensive mutation analysis. The method is entirely based on mathematics and it provides useful insight into how spectral analysis of Boolean functions can benefit software testing

On the Analysis of Boolean Functions and Fourier-Entropy-Influence Conjecture

This manuscript includes some classical results we select apart from the new results we've found on the Analysis of Boolean Functions and Fourier-Entropy-Influence conjecture. We try to ensure the self-completeness of this work so that readers could probably read it independently. Among the new results, what is the most remarkable is that we prove that the entropy of a boolean function $f$ could be upper bounded by $O(I(f))+O(\sum_{k}I_k(f)\log (1/I_k(f)))$. This is possibly the only untrivial bound for the entropy up to now

Harmonic analysis of neural networks

Neural networks models have attracted a lot of interest in recent years mainly because there were perceived as a new idea for computing. These models can be described as a network in which every node computes a linear threshold function. One of the main difficulties in analyzing the properties of these networks is the fact that they consist of nonlinear elements. I will present a novel approach, based on harmonic analysis of Boolean functions, to analyze neural networks. In particular I will show how this technique can be applied to answer the following two fundamental questions (i) what is the computational power of a polynomial threshold element with respect to linear threshold elements? (ii) Is it possible to get exponentially many spurious memories when we use the outer-product method for programming the Hopfield model

MCMC Learning

The theory of learning under the uniform distribution is rich and deep, with connections to cryptography, computational complexity, and the analysis of boolean functions to name a few areas. This theory however is very limited due to the fact that the uniform distribution and the corresponding Fourier basis are rarely encountered as a statistical model. A family of distributions that vastly generalizes the uniform distribution on the Boolean cube is that of distributions represented by Markov Random Fields (MRF). Markov Random Fields are one of the main tools for modeling high dimensional data in many areas of statistics and machine learning. In this paper we initiate the investigation of extending central ideas, methods and algorithms from the theory of learning under the uniform distribution to the setup of learning concepts given examples from MRF distributions. In particular, our results establish a novel connection between properties of MCMC sampling of MRFs and learning under the MRF distribution.Comment: 28 pages, 1 figur