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

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. © Springer-Verlag Berlin Heidelberg 2004.