Essence is a syntactically rich language for specifying search and optimization problems. We show how to applying descriptive complexity theory to study the expressive power of Essence, and present several results on the expressive power of fragments incorporating certain features. The same approach can be applied to a number of other constraint specification or modelling languages. We believe ...

Various ways of quantifying the nondeterminism in finite automata have been considered since the 1970’s. Roughly speaking, a nondeterminism measure can count the number of accepting computations (ambiguity), the number of all computations (computation width) or the amount of nondeterminism on a single best (or worst) computation on a given input. This paper surveys results on the growth rate of...

We show that for every rooted, finitely branching, pruned tree T of height ω there exists a family F which consists of order isomorphic to T subtrees of the dyadic tree C = {0, 1}<N with the following properties: (i) the family F is a Gδ subset of 2C ; (ii) every perfect subtree of C contains a member of F ; (iii) if K is an analytic subset of F , then for every perfect subtree S of C there exi...

Two of the most celebrated results that effectively exploit visual representation to give logical characterization and decidable modelchecking include visibly pushdown automata (VPA) by Alur and Madhusudan and event-clock automata (ECA) by Alur, Fix and Henzinger. VPA and ECA—by making the call-return edges visible and by making the clock-reset operation visible, respectively—recover decidabili...

This is a survey of results in descriptive set theory for domains and similar spaces, with the emphasis on the ω-algebraic domains. We try to demonstrate that the subject is interesting in its own right and is closely related to some areas of theoretical computer science. Since the subject is still in its beginning, we discuss in detail several open questions and possible future development. We...