Comparing two-dimensional one-marker automata to sgraffito automata

Authors:
Daniel Průša;František Mráz;Friedrich Otto
Affiliations:
Faculty of Electrical Engineering, Department of Cybernetics, Center for Machine Perception, Czech Technical University, Prague 2, Czech Republic;Faculty of Mathematics and Physics, Department of Computer Science, Charles University, Prague 1, Czech Republic;Fachbereich Elektrotechnik/Informatik, Universität Kassel, Kassel, Germany
Venue:
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
Year:
2013

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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.