An Undecidable Property of Recurrent Double Sequences
Mihai Prunescu · Notre Dame Journal of Formal Logic · 2008
For an arbitrary finite algebra A , f ⋅ ⋅ , 0 , 1 one defines a double sequence a i j by a i 0 = a 0 j = 1 and a i j = f a i , j - 1 , a i - 1 , j . The problem if such recurrent double sequences are ultimately zero is undecidable, even if we restrict it to the class of commutative finite algebras.