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A Note on the Emptiness of Semigroup Intersections.
- Source :
-
Fundamenta Informaticae . 2007, Vol. 79 Issue 1-2, p1-4. 4p. - Publication Year :
- 2007
-
Abstract
- We consider decidability questions for the emptiness problem of intersections of matrix semigroups. This problem was studied by A. Markov [7] and more recently by V. Halava and T. Harju [5]. We give slightly strengthened results of their theorems by using a different matrix encoding. In particular, we show that given two finitely generated semigroups of non-singular upper triangular 3 × 3 matrices over the natural numbers, checking the emptiness of their intersections is undecidable. We also show that the problem is undecidable even for unimodular matrices over 3 × 3 rational matrices. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATRICES (Mathematics)
*SEMIGROUPS (Algebra)
*GROUP theory
*MATHEMATICS
*ARITHMETIC
Subjects
Details
- Language :
- English
- ISSN :
- 01692968
- Volume :
- 79
- Issue :
- 1-2
- Database :
- Academic Search Index
- Journal :
- Fundamenta Informaticae
- Publication Type :
- Academic Journal
- Accession number :
- 26554509