Simple picture processing based on finite automata and regular grammars

Abstract

We are introducing and discussing finite automata working on rectangular-shaped arrays (i.e., pictures) in a boustrophedon reading mode. We prove close relationships with the well-established class of regular matrix (picture) languages. We derive several combinatorial, algebraic and decidability results for the corresponding class of picture languages. For instance, we show pumping and interchange lemmas for our picture language class. We also explain similarities and differences to the status of decidability questions for classical finite string automata. For instance, the non-emptiness problem for our picture-processing automaton model turns out to be NP-complete. Finally, we sketch possible applications to character recognition.