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On Reachability Problems for Low-Dimensional Matrix Semigroups

2019/02/28 by Thomas Colcombet, Joël Ouaknine, Pavel Semukhin +1 · 1 citation
Computer Science · #cs.CC #cs.FL

paper · pdf · doi:10.4230/lipics.icalp.2019.39

Full version of the paper submitted to ICALP 2019

arxiv created 2019/04/29 · arxiv updated 2019/04/30

Abstract

We consider the Membership and the Half-Space Reachability problems for matrices in dimensions two and three. Our first main result is that the Membership Problem is decidable for finitely generated sub-semigroups of the Heisenberg group over rational numbers. Furthermore, we prove two decidability results for the Half-Space Reachability Problem. Namely, we show that this problem is decidable for sub-semigroups of GL(2,ℤ) and of the Heisenberg group over rational numbers.

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