Based on different concepts to obtain a finer notion of language recognition via finite monoids we develop an algebraic structure called typed monoid.
This leads to an algebraic description of regular and non regular languages.

We obtain for each language a unique minimal recognizing typed monoid, the typed syntactic monoid.
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We prove that any propagating E0L system cannot generate the language containing all words of the form w#w. This result, together with some known ones, enable us to conclude that the flip-pushdown automata with k pushdown reversals (i.e. the pushdown automata with the ability to flip its pushdown) and E0L ... more >>>

We give a simpler proof, via query elimination, of a result due to O'Donnell, Saks, Schramm and Servedio, which shows a lower bound on the zero-error randomized query complexity of a function $f$ in terms of the maximum influence of any variable of $f$. Our lower bound also applies to ... more >>>