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<p><b>Abstract</b>—This paper studies theoretical aspects of one-dimensional linear hybrid cellular automata over a finite (Galois) field. General results concerning the characteristic polynomials of such automata are presented. A probabilistic synthesis algorithm for determining such a linear hybrid cellular automaton with a specific characteristic polynomial is given, along with empirical results and a theoretical analysis. Cyclic-boundary cellular automata are defined and related to the more common null-boundary cellular automata. An explicit similarity transform between a cellular automaton and its corresponding linear feedback shift register is derived.</p>
Cellular automata, characteristic polynomial, finite field, LFSM.
Kevin Cattell, Jon C. Muzio, "Analysis of One-Dimensional Linear Hybrid Cellular Automata over GF(q)", IEEE Transactions on Computers, vol. 45, no. , pp. 782-792, July 1996, doi:10.1109/12.508317
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