Varieties of recognizable tree series over fields

Weighted Automaton and Varieties of Formal Power Series

“…Petković [3] discussed varieties of fuzzy languages, varieties of ordinary languages and varieties of finite monoids. Fülöp and Tteinby [4] established a bijective correspondence between varieties of finite dimensional KΣ −algebras and varieties of recognizable Σ −tree series over a field K and a finite alphabet Σ .…”