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Full-Text Articles in Computer Sciences
Enhancements To Crisp Possibilistic Reconstructability Analysis, Anas Al-Rabadi, Martin Zwick
Enhancements To Crisp Possibilistic Reconstructability Analysis, Anas Al-Rabadi, Martin Zwick
Systems Science Faculty Publications and Presentations
Modified Reconstructibility Analysis (MRA), a novel decomposition within the framework of set-theoretic (crisp possibilistic) Reconstructibility Analysis, is presented. It is shown that in some cases while 3-variable NPN-classified Boolean functions are not decomposable using Conventional Reconstructibility Analysis (CRA), they are decomposable using Modified Reconstructibility Analysis (MRA). Also, it is shown that whenever a decomposition of 3-variable NPN-classified Boolean functions exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. A comparison of the corresponding complexities for Ashenhurst-Curtis decompositions, and Modified Reconstructibility Analysis (MRA) is also presented. While both AC and MRA decompose some but …
A Software Architecture For Reconstructability Analysis, Kenneth Willett, Martin Zwick
A Software Architecture For Reconstructability Analysis, Kenneth Willett, Martin Zwick
Systems Science Faculty Publications and Presentations
Software packages for reconstructability analysis (RA), as well as for related log linear modeling, generally provide a fixed set of functions. Such packages are suitable for end‐users applying RA in various domains, but do not provide a platform for research into the RA methods themselves. A new software system, Occam3, is being developed which is intended to address three goals which often conflict with one another to provide: a general and flexible infrastructure for experimentation with RA methods and algorithms; an easily‐configured system allowing methods to be combined in novel ways, without requiring deep software expertise; and a system which …
A Comparison Of Modified Reconstructability Analysis And Ashenhurst‐Curtis Decomposition Of Boolean Functions, Anas Al-Rabadi, Marek Perkowski, Martin Zwick
A Comparison Of Modified Reconstructability Analysis And Ashenhurst‐Curtis Decomposition Of Boolean Functions, Anas Al-Rabadi, Marek Perkowski, Martin Zwick
Systems Science Faculty Publications and Presentations
Modified reconstructability analysis (MRA), a novel decomposition technique within the framework of set‐theoretic (crisp possibilistic) reconstructability analysis, is applied to three‐variable NPN‐classified Boolean functions. MRA is superior to conventional reconstructability analysis, i.e. it decomposes more NPN functions. MRA is compared to Ashenhurst‐Curtis (AC) decomposition using two different complexity measures: log‐functionality, a measure suitable for machine learning, and the count of the total number of two‐input gates, a measure suitable for circuit design. MRA is superior to AC using the first of these measures, and is comparable to, but different from AC, using the second.
Modified Reconstructability Analysis For Many-Valued Functions And Relations, Anas Al-Rabadi, Martin Zwick
Modified Reconstructability Analysis For Many-Valued Functions And Relations, Anas Al-Rabadi, Martin Zwick
Systems Science Faculty Publications and Presentations
A novel many-valued decomposition within the framework of lossless Reconstructability Analysis is presented. In previous work, Modified Recontructability Analysis (MRA) was applied to Boolean functions, where it was shown that most Boolean functions not decomposable using conventional Reconstructability Analysis (CRA) are decomposable using MRA. Also, it was previously shown that whenever decomposition exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. In this paper, MRA is extended to many-valued logic functions, and logic structures that correspond to such decomposition are developed. It is shown that many-valued MRA can decompose many-valued functions when CRA fails to do …
Directed Extended Dependency Analysis For Data Mining, Thaddeus T. Shannon, Martin Zwick
Directed Extended Dependency Analysis For Data Mining, Thaddeus T. Shannon, Martin Zwick
Systems Science Faculty Publications and Presentations
Extended dependency analysis (EDA) is a heuristic search technique for finding significant relationships between nominal variables in large data sets. The directed version of EDA searches for maximally predictive sets of independent variables with respect to a target dependent variable. The original implementation of EDA was an extension of reconstructability analysis. Our new implementation adds a variety of statistical significance tests at each decision point that allow the user to tailor the algorithm to a particular objective. It also utilizes data structures appropriate for the sparse data sets customary in contemporary data mining problems. Two examples that illustrate different approaches …
Reconstructability Analysis Detection Of Optimal Gene Order In Genetic Algorithms, Martin Zwick, Stephen Shervais
Reconstructability Analysis Detection Of Optimal Gene Order In Genetic Algorithms, Martin Zwick, Stephen Shervais
Systems Science Faculty Publications and Presentations
The building block hypothesis implies that genetic algorithm efficiency will be improved if sets of genes that improve fitness through epistatic interaction are near to one another on the chromosome. We demonstrate this effect with a simple problem, and show that information-theoretic reconstructability analysis can be used to decide on optimal gene ordering.
Reversible Modified Reconstructability Analysis Of Boolean Circuits And Its Quantum Computation, Anas Al-Rabadi, Martin Zwick
Reversible Modified Reconstructability Analysis Of Boolean Circuits And Its Quantum Computation, Anas Al-Rabadi, Martin Zwick
Systems Science Faculty Publications and Presentations
Modified Reconstructability Analysis (MRA) can be realized reversibly by utilizing Boolean reversible (3,3) logic gates that are universal in two arguments. The quantum computation of the reversible MRA circuits is also introduced. The reversible MRA transformations are given a quantum form by using the normal matrix representation of such gates. The MRA-based quantum decomposition may play an important role in the synthesis of logic structures using future technologies that consume less power and occupy less space.
An Overview Of Reconstructability Analysis, Martin Zwick
An Overview Of Reconstructability Analysis, Martin Zwick
Systems Science Faculty Publications and Presentations
This paper is an overview of reconstructability analysis (RA), a discrete multivariate modeling methodology developed in the systems literature; an earlier version of this tutorial is Zwick (2001). RA was derived from Ashby (1964), and was developed by Broekstra, Cavallo, Cellier Conant, Jones, Klir, Krippendorff, and others (Klir, 1986, 1996). RA resembles and partially overlaps log‐line (LL) statistical methods used in the social sciences (Bishop et al., 1978; Knoke and Burke, 1980). RA also resembles and overlaps methods used in logic design and machine learning (LDL) in electrical and computer engineering (e.g. Perkowski et al., 1997). Applications of RA, like …
Reconstructability Analysis With Fourier Transforms, Martin Zwick
Reconstructability Analysis With Fourier Transforms, Martin Zwick
Systems Science Faculty Publications and Presentations
Fourier methods used in two‐ and three‐dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance‐type measure instead of information‐theoretic uncertainty, but the two measures are roughly collinear and the Fourier approach yields results close to that of standard RA. The Fourier method, however, does not require iterative calculations for models with loops. Moreover, the error in Fourier RA models can be assessed without actually generating the full probability distributions of the models; calculations scale with the size of the data rather than the state space. State‐based modeling using the Fourier approach is also …
State-Based Reconstructability Analysis, Martin Zwick, Michael S. Johnson
State-Based Reconstructability Analysis, Martin Zwick, Michael S. Johnson
Systems Science Faculty Publications and Presentations
Reconstructability analysis (RA) is a method for detecting and analyzing the structure of multivariate categorical data. While Jones and his colleagues extended the original variable‐based formulation of RA to encompass models defined in terms of system states, their focus was the analysis and approximation of real‐valued functions. In this paper, we separate two ideas that Jones had merged together: the “g to k” transformation and state‐based modeling. We relate the idea of state‐based modeling to established variable‐based RA concepts and methods, including structure lattices, search strategies, metrics of model quality, and the statistical evaluation of model fit for analyses based …