The first order convergence law fails for random perfect graphs

We consider first order expressible properties of random perfect graphs. That is, we pick a graph $G_n$ uniformly at random from all (labelled) perfect graphs on $n$ vertices and consider the probability that it satisfies some graph property that can be expressed in the first order language of graphs. We show that there exists such a first order expressible property for which the probability that $G_n$ satisfies it does not converge as $n\to\infty$.Comment: 11 pages. Minor corrections since last versio

Kl+ 1-free graphs: asymptotic structure and A 0-1 law

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel C 154061 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Adding for-Loops to First-Order Logic

We study the query language BQL: the extension of the relational algebra with for-loops. We also study FO(FOR): the extension of rst-order logic with a for-loop variant of the partial xpoint operator. In contrast to the known situation with query languages which include while-loops instead of for-loops, BQL and FO(FOR) are not equivalent. Among the topics we investigate are: the precise relationship between BQL and FO(FOR); inationary versus non-inationary iteration; the relationship with logics that have the ability to count; and nested versus unnested loops. 1 Introduction Much attention in database theory (or nite model theory) has been devoted to extensions of rst-order logic as a query language [AHV95, EF95]. A seminal paper in this context was that by Chandra in 1981 [Cha81], where he added various programming constructs to the relational algebra and compared the expressive power of the various extensions thus obtained. One such extension is the language that we d..