We give a general framework connecing a branching time relation on nodes of a transition system to a final coalgebra for a suitable endofunctor. Examples of relations treated by our theory include bisimilarity, similarity, upper and lower similarity for transition systems with divergence, similarity for discrete probabilistic systems, and nested similarity. Our results describe firstly how to c...

A relative one-relator presentation has the form P = 〈x,H;R〉 where x is a set, H is a group, and R is a word on x±1 ∪H. We show that if the word on x±1 obtained from R by deleting all the terms from H has what we call the unique max-min property, then the group defined by P is residually finite if and only if H is residually finite (Theorem 1). We apply this to obtain new results concerning the...

This paper presents an experiment analyzing the behavior of modelers in interpreting conceptual model fragments developed using an OntologyDriven Conceptual Modeling Language (OntoUML). Our goal is to evaluate the effect of two ontological constructs (relator and role) in modeling relationships. Our hypotheses are: (i) the use of these constructs for modeling relations increases the clarity of ...

In the article, a result relating to maps (= finite planar connected and simply connected 2-complexes) that satisfy a C(p)&T (q) condition (where (p, q) is one of (3, 6), (4, 4), (6, 3) which correspond to regular tessellations of the plane by triangles, squares, hexagons, respectively) is proven. On the base of this result a criterion for the Gromov hyperbolicity of finitely presented small ca...

The tunnel number of a PL knot K is the minimum number of PL one-cells which must be attached in order that the regular neighborhood of the resulting complex has complement a handlebody [2]. It is easy to see that n-bridge knots have tunnel numbers (n 1) and torus knots have tunnel number one. More difficult is finding knots which have higher tunnel number. If a knot has tunnel number one, it w...