This thesis contributes to the study of families of finitely presented infinite graphs,their structural properties and their relations to each other. Given a finite alpha-bet Σ, a Σ-labeled infinite graph can be characterized as a finite set of binaryrelations (Ra)a∈Σ over an arbitrary countable domain V . There are many ways tofinitely characterize such sets of relations, eithe...

Advanced temporal and spatial applications require both the representation of complex objects and the ability to nitely represent innnite relations. Representing such data requires combining the constraint relational model (allowing nite representation of innnite information) and either the nested relational or the object-oriented model (allowing representation of complex objects). In this pape...

We prove that proper coloring distinguishes between block-factors and finitely dependent stationary processes. A stochastic process is finitely dependent if variables at sufficiently wellseparated locations are independent; it is a block-factor if it can be expressed as a finite-range function of independent variables. The problem of finding non-block-factor finitely dependent processes dates b...

We construct an embedding of a free Burnside group B(m, n) of odd n > 2 and rank m > 1 in a finitely presented group with some special properties. The main application of this embedding is an easy construction of finitely presented non-amenable groups without noncyclic free subgroups (which provides a finitely presented counterexample to the von Neumann problem on amenable groups). As another a...

We study generalized multisets (multisets that allow possible negative multiplicities) both in the Zermelo-Fraenkel framework and in the finitely supported mathematics. We extend the notion of generalized multiset over a finite alphabet, and we replace it by the notion of algebraically finitely supported generalized multiset over a possibly infinite alphabet. We analyze the correspondence betwe...

We give characterizations of the property of being weakly reductive for finitely generated commutative semigroups. As a consequence of these characterizations we obtain an algorithm for determining from a presentation of a finitely generated commutative semigroup whether it is weakly reductive. Furthermore, we present some connections between cancellative finitely generated commutative semigrou...