Comparing Two-Dimensional One-Marker Automata to Sgraffito Automata

Abstract

We compare two types of automata for accepting picture languages to each other: the two-dimensional one-marker automaton and the sgraffito automaton. On the one hand, it is shown that deterministic sgraffito automata are strictly more powerful than deterministic two-dimensional one-marker automata. On the other hand, nondeterministic two-dimensional one-marker automata accept some picture languages that cannot be accepted by sgraffito automata. However, if nondeterministic two-dimensional one-marker automata were to accept all picture languages that are accepted by (deterministic) sgraffito automata, then the complexity classes NL (nondeterministic logarithmic space) and P (deterministic polynomial time) would coincide. Accordingly, it is likely that the classes of picture languages accepted by these two types of nondeterministic automata are incomparable under inclusion.