It is a well-known result of Fagin that the complexity class NP coincides with the class of problems expressible in existential second-order logic (1 ;). Monadic NP is the class of problems expressible in monadic Z;, i.e., 1: with the restriction that the second-order quantifiers range only over sets (as opposed to ranging over, say, binary relations). We prove that connectivity of finite graph...

We give a survey of the expressive power of various monadic logics on specific classes of finite labeled graphs, including words, trees, and pictures. Among the logics we consider, there are monadic secondorder logic and its existential fragment, the modal mu-calculus, and monadic least fixed-point logic. We focus on nesting-depth and quantifier alternation as a complexity measure of these logics.

Monadic second-order unification is second-order unification where all function constants occurring in the equations are unary. Here we prove that the problem of deciding whether a set of monadic equations has a unifier is NP-complete, where we use the technique of compressing solutions using singleton context-free grammars. We prove that monadic second-order matching is also NP-complete.

We show every monadic Heyting algebra is isomorphic to a functional monadic Heyting algebra. This solves a 1957 problem of Monteiro and Varsavsky [9].

In this paper we investigate effective descent morphisms in categories of reflexive and transitive lax algebras. We show in particular that open and proper maps are effective descent, result that extends the corresponding results for the category of topological spaces and continuous maps. Introduction A morphism p : E → B in a category C with pullbacks is called effective descent if it allows a...

In 1974 R. Fagin proved that properties of structures which are in NP are exactly the same as those expressible by existential second order sentences, that is sentences of the form: there exist such that , where is a tuple of relation symbols. and is a first order formula. Fagin was also the first to study monadic NP: the class of properties expressible by existential second order sentences whe...