On subsumption and semiunification in feature algebras

AbstractWe consider a generalization of term subsumption, or matching, to a class of mathematical structures which we call feature algebras. We show how these generalize both first-order terms and the feature structures used in computational linguistics. The notion of term subsumption generalizes to a natural notion of algebra homomorphism. In the setting of feature algebras, unification, corresponds naturally to solving constraints involving equalities between strings of unary function symbols, and semiunification also allows inequalities representing subsumption constraints. Our generalization allows us to show that the semiunification problem for finite feature algebras is undecidable. This implies that the corresponding problem for rational trees (cyclic terms) is also undecidable

Investigations into the Universal Algebra of Hypergraph Coverings and Applications

This thesis deals with two topics: acyclic covers and extension problems. The first part of the thesis deals with unbranched covers of graphs. The general theory of unbranched covers is discussed and then generalized to granular covers. Covers of this type maintain fixed structures of the covered graph. It is shown how unbranched covers of hypergraphs can be reduced to granular covers. With the help of further results we can identify the class of hypergraphs that have acyclic unbranched covers. The second part of the paper deals with extension problems. An extension problems it is about finitely extending finite structures so that partial automorphisms of the initial structure can be completed on the extension. We discuss classical results and reformulate them so that they are suitable for an algebraic characterization. These can be used to get new results regarding extension problems