On the Identity Problem for Unitriangular Matrices of Dimension Four

2022/02/10 by Ruiwen Dong, Dong, Ruiwen
Computer Science · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Symbolic Computation (cs.SC) #cs.DM #cs.SC

paper · pdf · doi:10.48550/arxiv.2202.05225

28 pages, 2 figures

arxiv created 2022/06/24 · arxiv updated 2022/06/27

Abstract

We show that the Identity Problem is decidable in polynomial time for finitely generated sub-semigroups of the group UT(4, ℤ) of 4 × 4 unitriangular integer matrices. As a byproduct of our proof, we also show the polynomial-time decidability of several subset reachability problems in UT(4, ℤ).

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