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<p><b>Abstract</b>—This paper introduces a new class of two-dimensional linear cellular automata and derives a number of their properties. A recursive relation is proved which enables the characteristic polynomial to be efficiently calculated, and minimal cost, maximal length generators of this type are listed for sizes up to 500. A theoretical analysis of the two vector transition properties of the cellular automata is given and it is shown that, for testing sequential faults over a set of standard benchmarks, the two-dimensional cellular automata perform, on average, better than one-dimensional linear hybrid cellular automata, and much better than linear finite shift registers.</p>
Linear hybrid cellular automata, linear finite state machine, maximum length cycle, primitive polynomial.
Kevin Cattell, Shujian Zhang, Micaela Serra, Jon C. Muzio, "2-by-n$n$ Hybrid Cellular Automata with Regular Configuration: Theory and Application", IEEE Transactions on Computers, vol. 48, no. , pp. 285-295, March 1999, doi:10.1109/12.754995
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