A Generalization of Strassen’s Theorem on Preordered Semirings

Abstract Given a commutative semiring with compatible preorder satisfying version of the Archimedean property, asymptotic spectrum, as introduced by Strassen (J. reine angew. Math. 1988), is an essentially unique compact Hausdorff space together map from to ring continuous functions. Strassen’s theorem characterizes relaxation that asymptotically compares large powers elements up subexponential factor pointwise partial order corresponding functions, realizing spectrum monotone homomorphisms nonnegative real numbers. Such preordered semirings have found applications in complexity theory and information theory. We prove generalization this satisfy weaker polynomial growth condition. This hypothesis does not ensure itself real-valued characterize (appropriate modification the) preorder. find sufficient condition well equivalent for hold. Under these conditions locally similar universal property work.