SOFSEM 2016: Theory and Practice of Computer Science

Kurganskyy, O and Potapov, I (2016) SOFSEM 2016: Theory and Practice of Computer Science. SOFSEM 2016: Theory and Practice of Computer Science, 9587.

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Abstract

Piecewise affine maps (PAMs) are frequently used as a reference model to show the openness of the reachability questions in other systems. The reachability problem for one-dimentional PAM is still open even if we define it with only two intervals. As the main contribution of this paper we introduce new techniques for solving reachability problems based on p-adic norms and weights as well as showing decidability for two classes of maps. Then we show the connections between topological properties for PAM’s orbits, reachability problems and representation of numbers in a rational base system. Finally we show a particular instance where the uniform distribution of the original orbit may not remain uniform or even dense after making regular shifts and taking a fractional part in that sequence.

Item Type:	Article
Uncontrolled Keywords:	Reachability problems, piecewise affine maps (PAMs), �-, expansion, p-adic analysis
Subjects:	?? QA ?? ?? QA75 ??
Depositing User:	Symplectic Admin
Date Deposited:	11 Dec 2015 11:17
Last Modified:	17 Dec 2022 01:17
DOI:	10.1007/978-3-662-49192-8
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/2039323