Abstract
We study connections between products of matrices and recursively enumerable sets. We show that for any positive integers m and n there exist three matrices M,N,B and a positive integer q such that if L is any recursively enumerable set of m×n matrices over nonnegative integers, then there is a matrix A such that the matrices in L are the nonnegative matrices in the set {AMm1NMm2N⋯NMmqB|m1,…,mq≥0}. We use this result to deduce an undecidability result for products of matrices which can be viewed as a variant of Rice's theorem stating that all nontrivial properties of recursively enumerable sets are undecidable.
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