Generation of Finite Inductive, Pseudo Random, Binary Sequences


Paul Fisher, Nawaf Aljohani, Jinsuk Baek, Journal of Information Processing Systems Vol. 13, No. 6, pp. 1554-1574, Dec. 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
[APA Style]
Paul Fisher, Nawaf Aljohani, & Jinsuk Baek (2017). Generation of Finite Inductive, Pseudo Random, Binary Sequences. Journal of Information Processing Systems, 13(6), 1554-1574. DOI: 10.3745/JIPS.01.0021.

[IEEE Style]
P. Fisher, N. Aljohani and J. 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. 2017. Generation of Finite Inductive, Pseudo Random, Binary Sequences. Journal of Information Processing Systems, 13, 6, (2017), 1554-1574. DOI: 10.3745/JIPS.01.0021.