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On the Identity Problem for Unitriangular Matrices of Dimension Four

Author Ruiwen Dong

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Ruiwen Dong
  • Department of Computer Science, University of Oxford, UK

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Ruiwen Dong. On the Identity Problem for Unitriangular Matrices of Dimension Four. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.MFCS.2022.43

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).

Subject Classification

ACM Subject Classification
  • Computing methodologies → Symbolic and algebraic manipulation
Keywords
  • identity problem
  • matrix semigroups
  • unitriangular matrices

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