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articleNo Access
ON FREE SPECTRA OF VARIETIES OF LOCALLY THRESHOLD TESTABLE SEMIGROUPS
- IGOR DOLINKA
International Journal of Algebra and Computation31 Aug 2012
Preview Abstract
A semigroup S is said to be ℓ-threshold k-testable if it satisfies all identities u = v where u, v is an arbitrary pair of words over a finite alphabet Σ such that they simultaneously belong or fail to belong to any ℓ-threshold k-testable (regular) language. We give an asymptotic formula for the free spectrum of the variety of all ℓ-threshold k-testable semigroups, thereby providing an asymptotic upper bound on the size of an arbitrary finitely generated locally threshold testable semigroup. The combinatorial interpretation of this task yields an enumeration problem for particular edge labelings of de Bruijn graphs.

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