On deterministic finite automata and syntactic monoid size
We investigate the relationship between regular languages and syntactic monoid size. In particular, we consider the transformation monoids of \(n\)-state (minimal) deterministic finite automata. We show tight upper and lower bounds on the syntactic monoid size depending on the number of generators (input alphabet size) used. It turns out, that the two generator case is the most involved one.
scientific article; zbMATH DE number 2126131
scientific article