By a well-known result due to Büchi and Trakhtenbrot, all monadic second-order sentences over words describe regular languages. In this paper, we investigate prefix classes of general second-order logic. Such a prefix class is called regular, if each of its sentences describes a regular language, and nonregular otherwise. Recently, the regular and nonregular prefix classes of existential second...

Hertrampf et al. (1993) looked at complexity classes which are characterized (say accepted) by a regular language for the words of output bits produced by nondeterministic polynomial-time computations. A number of well-known complexity classes between P and PSPACE are accepted by regular languages. For example, NP is accepted by the regular language which consists of the words which contain at ...