Matricial Iteration Theories
Recall the definition of matricial theories from Section 3.5.3. Since each matricial theory can be represented as a theory Matr(S; V) for some semiring module pair (S;V), we will be considering only matricial theories of this sort. A matricial iteration theory is a matricial theory which is simultaneously an iteration theory. We show that when T = Matr(S; V) is a matricial iteration theory, the dagger operation determines and is determined by a star operation on the semiring S and an omega operation ω: S → V from the semiring to the module.
KeywordsExtension Theorem Base Matrix Regular Language Pairing Identity Iteration Theory
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