Iterative and recursive matrix theories

David B Benson, Irène Guessarian
1984 Journal of Algebra  
TO THE MEMORY OF CALVIN C. ELGOT Matrix theories are algebraic theories (in the sense of Lawvere) in which each morphism p: [m] + [n] is an m x n matrix of morphisms pij : [ 1 ] + [ 11. We develop the iterative matrix theories in which systems of linear equations have solutions and the recursive matrix theories in which systems of polynomial equations have solutions. There are intimate connections with formal power series as developed in formal language theory: the iterative matrix theories are
more » ... based on rational sets of formal power series and the recursive matrix theories are based on algebraic sets of formal power series. The motivation is the applications of these matrix theories to the study of computer program behavior.
doi:10.1016/0021-8693(84)90035-8 fatcat:h6xlk26gibgdbehkxd7rqrkdkm