Abstract
We propose a framework for pattern matching in two-dimensional arrays of symbols where the patterns are described by an extended version of the regular matrix grammar and the size of desired matches is prescribed. We then demonstrate how to reformulate the 2D pattern matching as the one-dimensional pattern matching (string pattern matching), and study the efficiency of the string pattern matching algorithm based on pattern complexity with respect to two finite automaton models: (1) the classical finite automaton and (2) the finite automaton equipped with two scanning heads placed in a fixed distance. We also identify several subclasses of the considered templates for which the framework yields a more efficient matching than the naive algorithm.
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