Matrix iteration theories are characterized by identities using theory operations as well as a star operation on T(n, n), for each n ≥ 0. The initial matrix iteration theory is described explicitly. An extension theorem is proved which implies that if MatS is a matrix iteration theory, so is MatR where R is a semiring of formal power series over S. In Part II these results are extended to Elgot's matricial theories.
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics