A survey on picture-walking automata

Authors:
Jarkko Kari;Ville Salo
Affiliations:
Department of Mathematics, University of Turku, Turku, Finland;Department of Mathematics, University of Turku, Turku, Finland
Venue:
Algebraic Foundations in Computer Science
Year:
2011

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Abstract

Picture walking automata were introduced by M. Blum and C. Hewitt in 1967 as a generalization of one-dimensional two-way finite automata to recognize pictures, or two-dimensional words. Several variants have been investigated since then, including deterministic, non-deterministic and alternating transition rules; four-, three- and two-way movements; single- and multi-headed variants; automata that must stay inside the input picture, or that may move outside. We survey results that compare the recognition power of different variants, consider their basic closure properties and study decidability questions.