It is known that the languages definable by formulae of the logics FO2[<,S], 2[<,S], LTL[F,P,X,Y] are exactly the variety DAD. Automata for this class are not known, nor is i...
— This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Σ1 formulas. This is a tree extension of the Simon theorem,...