The \(k\)-cut number of rooted graphs was introduced by Cai et al. as a generalization the classical cutting model Meir and Moon. In this paper, we show that all moments conditioned Galton-Watson trees converge after proper rescaling, which implies convergence in distribution to same limit law regardless offspring trees. This extends result Janson. Using method, also various random or determini...

In the article Recursive queries on trees and data trees (ICDT’13), Abiteboul et al. asked whether the containment problem for monadic datalog over unordered unranked labeled trees using the child relation and the descendant relation is decidable. This note gives a positive answer to this question, as well as an overview of the relative expressive power of monadic datalog on various representat...

We investigate the complexity of finding solutions to infinite recursive constraint satisfaction problems. We show that, in general, the problem of finding a solution to an infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through a recursive tree. We also identify natural classes of infinite recursive constraint problems where the probl...

We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total variation point of view. To do this, we construct statistics that measure, in a certain well-defined sense, global “balancedness” properties of such trees. Our...

We describe a parameterized decision procedure that extends the decision procedure for functional recursive algebraic data types (trees) with the ability to specify and reason about abstractions of data structures. The abstract values are specified using recursive abstraction functions that map trees into other data types that have decidable theories. Our result yields a decidable logic which c...