Reachability problems in low-dimensional nondeterministic polynomial maps over integers



Ko, SK, Niskanen, R ORCID: 0000-0002-2210-1481 and Potapov, I
(2021) Reachability problems in low-dimensional nondeterministic polynomial maps over integers. INFORMATION AND COMPUTATION, 281. p. 104785.

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Abstract

We study reachability problems for various nondeterministic polynomial maps in Zn. We prove that the reachability problem for very simple three-dimensional affine maps (with independent variables) is undecidable and is PSPACE-hard for both two-dimensional affine maps and one-dimensional quadratic maps. Then we show that the complexity of the reachability problem for maps without functions of the form ±x+a0 is lower. In this case the reachability problem is PSPACE for any dimension and if the dimension is not fixed, then the problem is PSPACE-complete. Finally we extend the model by considering maps as language acceptors and prove that the universality problem is undecidable for two-dimensional affine maps.

Item Type: Article
Divisions: Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User: Symplectic Admin
Date Deposited: 28 Jun 2021 09:37
Last Modified: 18 Jan 2023 21:37
DOI: 10.1016/j.ic.2021.104785
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3127989