A new system called sequential/parallel matrix grammars for two-dimensional pattern processing is introduced and studied. Miscellaneous language operations such as union, catenation (row and column), Kleene's closure (row and column) and substitutions are investigated. The equivalence of sequential/parallel matrix languages and finite-turn repetitive checking automata is established. Hierarchies for both languages and machines are also found. We also give regular-like expressions and array grammars that describe sets of matrices or rectangular arrays with fixed proportions. Finally, several related future research topics are mentioned. The primary advantage of our model over others is that it provides a compromise between purely sequential methods, which take too much time for large arrays, and purely parallel methods, which usually take too much hardware for large arrays.
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On Sequential/parallel Matrix Array Languages
Patrick Shen-Pei Wang
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