Computation in one-dimensional piecewise maps

Authors:
Oleksiy Kurganskyy;Igor Potapov;Fernando Sancho Caparrini
Affiliations:
Institute of Applied Mathematics and Mechanics, NAS of Ukraine;Computer Science Department, University of Liverpool;Department of Computer Science and AI, University of Seville
Venue:
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Year:
2007

Citing 2
Cited 2

Widening the Boundary between Decidable and Undecidable Hybrid Systems

CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
Computation in one-dimensional piecewise maps and planar pseudo-billiard systems

UC'05 Proceedings of the 4th international conference on Unconventional Computation

On undecidability bounds for matrix decision problems

Theoretical Computer Science
Low dimensional hybrid systems - decidable, undecidable, don't know

Information and Computation

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Abstract

In this paper we show that the one-dimensional Piecewise Affine Maps (PAMs) are equivalent to planar Pseudo-Billiard Systems (PBSs) or so called "strange billiards". The reachability problem for PAMs is still open, however the more general model of rational one-dimensional maps is shown to be universal with undecidable reachability problem.