Undecidability in matrices over Laurent polynomials

Vesa Halava, Tero Harju
2004 Advances in Applied Mathematics  
We show that it is undecidable for finite sets S of upper triangular (4 × 4)-matrices over Z[x, x −1 ] whether or not all elements in the semigroup generated by S have a nonzero constant term in some of the Laurent polynomials of the first row. This result follows from a representations of the integer weighted finite automata by matrices over Laurent polynomials.
doi:10.1016/j.aam.2004.04.002 fatcat:m33bmnfsnjeghaclct5ouf2q4e