Weighted Branching Simulation Distance for Parametric Weighted Kripke Structures

Weighted Branching Systems: Behavioural Equivalence, Metric Structure, and their Characterisations

In this report, we extend the notion of branching bisimulation to weighted systems, more speci cally weighted Kripke structures. We show that a version weighted CTL that excludes the next-operator characterises this weighted branching bisimulation. Due to the restrictive nature of exact quantitative behavioural equivalences, we introduce a notion of expanding our bisimulation by allowing transi...

A Quantitative Characterization of Weighted Kripke Structures in Temporal Logic

We extend the usual notion of Kripke Structures with a weighted transition relation, and generalize the usual Boolean satisfaction relation of CTL to a map which assigns to states and temporal formulae a real-valued distance describing the degree of satisfaction. We describe a general approach to obtaining quantitative interpretations for a generic extension of the CTL syntax, and show that, fo...

Coupling on weighted branching trees

This paper considers linear functions constructed on two different weighted branching processes and provides explicit bounds for their Kantorovich-Rubinstein distance in terms of couplings of their corresponding generic branching vectors. Motivated by applications to the analysis of random graphs, we also consider a variation of the weighted branching process where the generic branching vector ...

On Symmetry of Some Nano Structures

It is necessary to generate the automorphism group of a chemical graph in computer-aided structure elucidation. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce...

An iterative approach for estimation of efficiency by weighted distance