Generation of Finite Inductive, Pseudo Random, Binary Sequences

Paul Fisher, Nawaf Aljohani and Jinsuk Baek
Volume: 13, No: 6, Page: 1554 ~ 1574, Year: 2017
10.3745/JIPS.01.0021
Keywords: Pseudo Random, Linear Shift Registers, Finite Induction, Graphs, Hamiltonian Cycles
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Abstract
This paper introduces a new type of determining factor for Pseudo Random Strings (PRS). This classification depends upon a mathematical property called Finite Induction (FI). FI is similar to a Markov Model in that it presents a model of the sequence under consideration and determines the generating rules for this sequence. If these rules obey certain criteria, then we call the sequence generating these rules FI a PRS. We also consider the relationship of these kinds of PRS’s to Good/deBruijn graphs and Linear Feedback Shift Registers (LFSR). We show that binary sequences from these special graphs have the FI property. We also show how such FI PRS’s can be generated without consideration of the Hamiltonian cycles of the Good/deBruijn graphs. The FI PRS’s also have maximum Shannon entropy, while sequences from LFSR’s do not, nor are such sequences FI random.

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Cite this article
IEEE Style
Paul Fisher, Nawaf Aljohani, and Jinsuk Baek, "Generation of Finite Inductive, Pseudo Random, Binary Sequences," Journal of Information Processing Systems, vol. 13, no. 6, pp. 1554~1574, 2017. DOI: 10.3745/JIPS.01.0021.

ACM Style
Paul Fisher, Nawaf Aljohani, and Jinsuk Baek, "Generation of Finite Inductive, Pseudo Random, Binary Sequences," Journal of Information Processing Systems, 13, 6, (2017), 1554~1574. DOI: 10.3745/JIPS.01.0021.