2-by-n hybrid cellular automata with regular configuration: theory and application

Abstract

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.