A Framework of Variant Logic Construction for Cellular Automata

Zheng, Jeffrey; Zheng, Christian; Kunii, Tosiyasu L.

doi:10.5772/15400

Cited by 11 publications

(4 citation statements)

References 12 publications

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“…As an example, the values T = 4 and V = 10 lead to the sequence Step D: From meta-measures to variant maps There are many possibilities to combine meta-measures for the creation of variant maps [3,[15][16][17][18][19][20][21]. To transform the bat echolocation calls into 2D color maps, we defined for each segment of meta-measures the axis values X = M + + M ⊥ and Y = M ⊥ + M − + M .…”

Section: Transformationmentioning

confidence: 99%

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Successful Creation of Regular Patterns in Variant Maps from Bat Echolocation Calls

Heim¹,

Heim²,

Zeng³

et al. 2018

Variant Construction From Theoretical Foundation to Applications

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We created variant maps based on bat echolocation call recordings and outline here the transformation process and describe the resulting visual features. The maps show regular patterns while characteristic features change when bat call recording properties change. By focusing on specific visual features, we found a set of projection parameters which allowed us to classify the variant maps into two distinct groups. These results are promising indicators that variant maps can be used as basis for new echolocation call classification algorithms.

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Section: Transformationmentioning

confidence: 99%

“…Our method to transform the bat call recordings is based on measures proposed by Zheng [15] in the 1990s to partition special phase spaces in binary image analysis. These methods were extended in the 2010s [3,16] and successfully used to classify quantum interactions [17,18], differently encrypted messages [19], and noncoding DNA [20,21].…”

Section: Introductionmentioning

confidence: 99%

Successful Creation of Regular Patterns in Variant Maps from Bat Echolocation Calls

Heim¹,

Heim²,

Zeng³

et al. 2018

Variant Construction From Theoretical Foundation to Applications

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“…In 1990s, Zheng [39,40] proposed conjugate classifications to apply seven invariants in a hierarchy to partition the kernels of four regular plane lattices on n = {4, 5, 7, 9} cases for 2D binary images. For n-tuple 0-1 vectors, variant logic frameworks [41,42] are proposed in 2010s, various applications are explored, such as 3D visual method [37], variant Pseudorandom Number Generator (PRNG) [38,43], computational simulation on quantum interactions [44][45][46][47] and non-coding DNA analysis [48][49][50].…”

Section: Variant Symmetric Schemes -Variant Invariantsmentioning

confidence: 99%

Symmetric Clusters in Hierarchy with Cryptographic Properties

Zheng

2018

Variant Construction From Theoretical Foundation to Applications

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Symmetric Boolean functions play a key role in stream ciphers. Symmetric constructions provide core components in cryptographic applications. In this chapter, four meta symmetric clustering schemes (combination, crossing, variant and rotation) are organized in a hierarchy for n variables of 0-1 vectors in measuring phase spaces. Local counting properties in a cluster and global counting properties in a given level are formulated. From selected symmetric clusters, a number of various symmetric Boolean functions are formulated. Counting properties on symmetric clusters, vectors in selected clusters and special symmetric Boolean functions are listed. Four sets of symmetric Boolean functions are compared. Properties of symmetric clusters and Boolean functions are discussed. Main results are expressed in theorems and tables. Among four meta schemes, the variant scheme presents novel properties approximately with O n 2 /4 clusters on a 2D phase space different from other schemes: combinatorial O (n), crossing O (n/2) and rotation O (2 n /n) on 1D measuring phase spaces, respectively. The variant pseudorandom number generator is a similar approach on RC4 and HC128 stream ciphers using word-oriented 0-1 vectors. Further advanced researches and explorations on relevant optimal configurations are required. Keywords Symmetric construction • Meta symmetric Cluster • hierarchy Boolean function • Four meta schemes • Phase space

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“…The current scheme is a derivative of the work of Zheng et al [16,17] to organize 1D 0-1 sequences as certain N > 1 length vectors using three parameters in variant measurement construction and classifications on hierarchical discrete phase spaces in general.…”

Section: Previous Workmentioning

confidence: 99%

Triangular Numbers and Their Inherent Properties

Zheng

2018

Variant Construction From Theoretical Foundation to Applications

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A method to classify one-dimensional binary sequences using three parameters intrinsic to the sequence itself is introduced. The classification scheme creates combinatorial patterns that can be arranged in a two-dimensional triangular structure. Projections of this structure contain interesting properties related to the Pascal triangle numbers. The arrangement of numbers within the triangular structure has been named "triangular numbers", and the essential parameters, elementary equation, and sequencing schemes are discussed as well as visualizations of sample distributions, special cases, and search results. We believe this to be a novel finding as sequences generated using this method are not contained in the On-Line Encyclopedia of Integer Sequences or OEIS.

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A Framework of Variant Logic Construction for Cellular Automata

Cited by 11 publications

References 12 publications

Successful Creation of Regular Patterns in Variant Maps from Bat Echolocation Calls

Successful Creation of Regular Patterns in Variant Maps from Bat Echolocation Calls

Symmetric Clusters in Hierarchy with Cryptographic Properties

Triangular Numbers and Their Inherent Properties

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