• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.1-10
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• 2001

We investigate the relationship between the 0-tree and other trees in linear nongroup cellular automata. And we show that given a 0-basic path of 0-tree and a nonzero attractor ${\alpha}$ of a multiple attractor linear cellulara automata with two predecessor we construct an ${\alpha}$-tree of that multiple attractor linear cellular automata.

• Journal of Korea Multimedia Society
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• v.4 no.1
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• pp.91-95
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• 2001

We investigate some properties of one dimensional linear nongroup cellular automata that have nonreachable states over GF(2). Specially we show interesting relationships between th states in a nonzero tree corresponding to each level state in the 0-tree.

• The Journal of the Korea institute of electronic communication sciences
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• v.10 no.5
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• pp.593-598
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• 2015

Non-linear cellular automata is difficult to analyze mathematically than linear cellular automata. So it is difficult to identify reachable states and attractors of nongroup non-linear cellular automata than nongroup linear cellular automata. In this paper, we propose a new reachable table to overcome these problems. We can see the next state for all the states of the non-linear cellular automata by the proposed reachable table. In addition, we can identify reachable states and attractors by the reachable table.

• Journal of Korea Multimedia Society
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• v.18 no.11
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• pp.1281-1288
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• 2015

Nongroup Cellular Automata(CA) having two trees in the state transition diagram of a CA is suitable for pattern classifier which divides pattern set into two classes. Maji et al. [1] classified patterns by using multiple attractor cellular automata as a pattern classifier with dependency vector. In this paper we propose a method of generation of a pattern classifier using feature vector which is the extension of dependency vector. In addition, we propose methods for finding nonreachable states in the 0-tree of the state transition diagram of TPMACA corresponding to the given feature vector for the analysis of the state transition behavior of the generated pattern classifier.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2007.06a
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• pp.423-426
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• 2007

In this paper, we propose an algorithm for finding 90/150 Two Predecessor Nongroup Cellular Automata(TPNCA). Especially, we synthesize TPNCA for the minimal polynomial whose type is of the form xp(x) or x(x+1)p(x) using the proposed algorithm which is useful to study pseudorandom number generation, where p(x) is some primitive polynomial. Also we synthesize Two Predecessor Single Attractor CA and Two Predecessor Multiple Attractor CA which are useful to study hashing.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.2
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• pp.105-111
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• 2005

Though GF(2) CA can only handle data with bit units GF(2p) CA can handle data with units more than bit units. In this paper we analyze the state-transition of nongroup cellular automata(CA) with a single attractor over GF(2p). And we propose the constructing method the state-transition diagram of a linear SACA over GF(2p) by using the concept of basic path. Also we propose the state-transition diagram of the nonlinear complemented SACA by using the state-transition diagram of a linear SACA.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1331-1342
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• 2009

In this paper, we analyze the behavior of the state transition of nongroup CA with a single attractor over GF($2^p$)(p > 1), and propose the algorithm for the construction of the state transition diagram of a Single Attractor CA(SACA) over GF($2^p$) which is very different from the construction algorithm for the state transition diagram of GF(2) SACA.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.6
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• pp.1047-1054
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• 2004

One of the fundamental problems in computer science is how to store information so that it can be searched and retrieved efficiently. Hashing is a technique which solves this problem. In this paper, we propose a tree construction algorithm using linear two-predecessor single attractor cellular automata C and its complemented cellular automata. Also by using the concept of MRT we give a perfect hasing algorithm based on C.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.9
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• pp.1939-1946
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• 2011

Expander graphs are useful in the design and analysis of communication networks. Mukhopadhyay et. al introduced a method to generate a family of expander graphs based on nongroup two predecessor single attractor CA(Cellular Automata). In this paper we propose a method to generate a family of expander graphs based on 60/102 Null boundary CA(NBCA) which is a group CA. The spectral gap generated by our method is larger than that of Mukhopadhyay et. al [12]. As an application we give an algorithm which generate one-way functions whose security lies on the combinatorial properties of our expander graphs. the one-way function using d-regular graph generated by the 60/102 NBCA is based on the Goldreich's construction [5].

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.335-338
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• 2005

Though GF(2) CA can only handle data with bit units, GF(2$^{p}$) CA can handle data with byte units. In this paper we analyze the state-transition of nongroup cellular automata(CA) with a single attractor over GF(2$^{p}$). And we propose the constructing method of the state-transition diagram of a linear SACA over GF(2$^{p}$) by using the concept of basic path. Also we propose the state-transition diagram of the nonlinear complemented SACA by using the state-transition diagram of a linear SACA.