On the computation power of finite automata in two-dimensional environments

Authors:
Oleksiy Kurganskyy;Igor Potapov
Affiliations:
Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, Donetsk, Ukraine;Department of Computer Science, University of Liverpool, Liverpool, U.K.
Venue:
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Year:
2004

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Abstract

In this paper we study the model of a finite state automaton interacting with infinite two-dimensional geometric environments. We show that the reachability problem for a finite state automaton interacting with a quadrant of the plane extended by a power function, a polynomial function or a linear function is algorithmically undecidable, by simulating a Minsky machine. We also consider the environment defined by a parabola which impedes the direct simulation of multiplication. However we show that the model of a finite automaton interacting inside a parabola is also universal.