Properties of Almost All Graphs and Generalized Quantifiers

Properties of Almost All Graphs and Generalized Quantifiers

We study 0-1 laws for extensions of first-order logic by Lindström quantifiers. We state sufficient conditions on a quantifier Q expressing a graph property, for the logic FO[Q] – the extension of first-order logic by means of the quantifier Q – to have a 0-1 law. We use these conditions to show, in particular, that FO[Rig], where Rig is the quantifier expressing rigidity, has a 0-1 law. We als...

On almost sure elimination of generalized quantifiers

Almost All Complex Quantifiers Are Simple

We prove that PTIME generalized quantifiers are closed under Boolean operations, iteration, cumulation and resumption.

Generalized Quantifiers for Simple Properties

We consider extensions of xed-point logic by means of generalized quantiiers in the context of descriptive complexity. By the well-known theorem of Immerman and Vardi, xed-point logic captures PTime over linearly ordered structures. It fails, however , to express even most fundamental structural properties, like simple cardinality properties, in the absence of order. In the present investigatio...

Set intersection representations for almost all graphs

Two variations of set intersection representation are investigated and upper and lower bounds on the minimum number of labels with which a graph may be represented are found which hold for almost all graphs. Speciically, if k (G) is deened to be the minimum number of labels with which G may be represented using the rule that two vertices are adjacent if and only if they share at least k labels,...