The Reachability Problem for Affine Functions on the Integers
Formal Languages and Automata Theory
2013-04-10 v1 Discrete Mathematics
Abstract
We consider the problem of determining, given x, y in Z^k and a finite set F of affine functions on Z^k, whether y is reachable from x by applying the functions F. We also consider the analogous problem over N^k. These problems are known to be undecidable for k >= 2. We give 2-EXPTIME algorithms for both problems in the remaining case k = 1. The exact complexities remain open, although we show a simple NP lower bound.
Keywords
Cite
@article{arxiv.1304.2639,
title = {The Reachability Problem for Affine Functions on the Integers},
author = {Daniel Fremont},
journal= {arXiv preprint arXiv:1304.2639},
year = {2013}
}
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13 pages