English

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}
}

Comments

13 pages

R2 v1 2026-06-21T23:56:40.356Z