scholarly journals Boolean Function Matching using Walsh Spectral Decision Diagrams

2006 ◽  
Author(s):  
Jason Moore ◽  
Kenneth Fazel ◽  
Mitchell Thornton ◽  
D. Miller
Keyword(s):  
Boolean Function ◽  
Decision Diagrams

scholarly journals Calculation of selection probabilities of stack filters through BDD

2004 ◽  
Vol 17 (3) ◽  
pp. 421-442
Author(s):  
Suzana Stojkovic ◽  
Jaakko Astola ◽  
Karen Egiazarian
Keyword(s):  
Boolean Function ◽  
Spectral Method ◽  
Binary Decision Diagrams ◽  
Decision Diagrams ◽  
Binary Decision ◽  
Stack Filters ◽  
Selection Probabilities ◽  
Exponential Complexity

This paper presents a procedure for calculation of selection probabilities of stack filters using Binary decision diagrams (BDDs) to represent the positive Boolean function that defines the stack filter. The procedure is derived by a modification of the spectral method for calculation of selection probabilities of stack filters. The usage of BDDs, instead of vectors overcomes the exponential complexity of the corresponding spectral method and extends application of the spectral method to stack filters with large windows widths.

scholarly journals Synthesis of quantum circuits based on incompletely specified functions and if-decision diagrams

2021 ◽  
pp. 84-97
Author(s):  
Anatoly A. Prihozhy
Keyword(s):  
Boolean Function ◽  
Quantum Circuit ◽  
Binary Decision Diagram ◽  
Quantum Circuits ◽  
Graph Representation ◽  
Decision Diagrams ◽  
Decomposition Products ◽  
Binary Decision ◽  
Binary Diagram ◽  
Functional Specification

The problem of synthesis and optimisation of logical reversible and quantum circuits from functional descriptions represented as decision diagrams is considered. It is one of the key problems being solved with the aim of creating quantum computing technology and quantum computers. A new method of stepwise transformation of the initial functional specification to a quantum circuit is proposed, which provides for the following project states: reduced ordered binary decision diagram, if-decision diagram, functional if-decision diagram, reversible circuit and quantum circuit. The novelty of the method consists in extending the Shannon and Davio expansions of a Boolean function on a single variable to the expansions of the same Boolean function on another function with obtaining decomposition products that are represented by incompletely defined Boolean functions. Uncertainty in the decomposition products gives remarkable opportunities for minimising the graph representation of the specified function. Instead of two outgoing branches of the binary diagram vertex, three outgoing branches of the if-diagram vertex are generated, which increase the level of parallelism in reversible and quantum circuits. For each transformation step, appropriate mapping rules are proposed that reduce the number of lines, gates and the depth of the reversible and quantum circuit. The comparison of new results with the results given by the known method of mapping the vertices of binary decision diagram into cascades of reversible and quantum gates shows a significant improvement in the quality of quantum circuits that are synthesised by the proposed method.

Dynamic minimization of bi-kronecker functional decision diagrams

2020 ◽  
Author(s):  
Xuanxiang Huang ◽  
Haipeng Che ◽  
Liangda Fang ◽  
Qingliang Chen ◽  
Quanlong Guan ◽  
...  
Keyword(s):  
Decision Diagrams

scholarly journals Comparison of Quantitative Morphology of Layered and Arbitrary Patterns: Contrary to Visual Perception, Binary Arbitrary Patterns Are Layered from a Structural Point of View

2021 ◽  
Vol 11 (14) ◽  
pp. 6300
Author(s):  
Igor Smolyar ◽  
Daniel Smolyar
Keyword(s):  
Boolean Function ◽  
Layer Structure ◽  
Central Element ◽  
Morphological Characteristics ◽  
Building Blocks ◽  
Point Of View ◽  
Living Systems ◽  
Seismic Profiles ◽  
Contour Maps ◽  
Anisotropic Layers

Patterns found among both living systems, such as fish scales, bones, and tree rings, and non-living systems, such as terrestrial and extraterrestrial dunes, microstructures of alloys, and geological seismic profiles, are comprised of anisotropic layers of different thicknesses and lengths. These layered patterns form a record of internal and external factors that regulate pattern formation in their various systems, making it potentially possible to recognize events in the formation history of these systems. In our previous work, we developed an empirical model (EM) of anisotropic layered patterns using an N-partite graph, denoted as G(N), and a Boolean function to formalize the layer structure. The concept of isotropic and anisotropic layers was presented and described in terms of the G(N) and Boolean function. The central element of the present work is the justification that arbitrary binary patterns are made up of such layers. It has been shown that within the frame of the proposed model, it is the isotropic and anisotropic layers themselves that are the building blocks of binary layered and arbitrary patterns; pixels play no role. This is why the EM can be used to describe the morphological characteristics of such patterns. We present the parameters disorder of layer structure, disorder of layer size, and pattern complexity to describe the degree of deviation of the structure and size of an arbitrary anisotropic pattern being studied from the structure and size of a layered isotropic analog. Experiments with arbitrary patterns, such as regular geometric figures, convex and concave polygons, contour maps, the shape of island coastlines, river meanders, historic texts, and artistic drawings are presented to illustrate the spectrum of problems that it may be possible to solve by applying the EM. The differences and similarities between the proposed and existing morphological characteristics of patterns has been discussed, as well as the pros and cons of the suggested method.

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