On Affine Reachability Problems
Computational Complexity
2020-07-03 v3 Formal Languages and Automata Theory
Abstract
We analyze affine reachability problems in dimensions 1 and 2. We show that the reachability problem for 1-register machines over the integers with affine updates is PSPACE-hard, hence PSPACE-complete, strengthening a result by Finkel et al. that required polynomial updates. Building on recent results on two-dimensional integer matrices, we prove NP-completeness of the mortality problem for 2-dimensional integer matrices with determinants +1 and 0. Motivated by tight connections with 1-dimensional affine reachability problems without control states, we also study the complexity of a number of reachability problems in finitely generated semigroups of 2-dimensional upper-triangular integer matrices.
Keywords
Cite
@article{arxiv.1905.05114,
title = {On Affine Reachability Problems},
author = {Stefan Jaax and Stefan Kiefer},
journal= {arXiv preprint arXiv:1905.05114},
year = {2020}
}