A Kleene Theorem for Free Many-Sorted AlgebrasResearch Paper
Kleene's theorem (Kleene 1956; McNaughton–Yamada 1960) is a cornerstone of formal language theory: over a free monoid, the languages recognized by finite automata are exactly the regular ones — those built from finite languages by union, concatenation, and the Kleene star. Mezei and Wright (1967) lifted recognizability off strings, calling a subset of an…