Combinatorial characterization of pseudometrics

Extensions of totally bounded pseudometrics

Clusters, Concepts, and Pseudometrics

The fields of cluster analysis and concept analysis are both used to identify patterns in data. Concept analysis identifies similarities between sets of objects based on their attributes. Cluster analysis groups objects with related characteristics based on some notion of distance. In this paper, we investigate connections between these two approaches. In particular, for each binary relation de...

Modal Characterisations of Behavioural Pseudometrics

For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on the Hennessy-Milner logic. The logic for characteris...

Behavioural Pseudometrics for Nondeterministic Probabilistic Systems

For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on Hennessy-Milner logic. The logic for characterising ...

A Combinatorial Characterization of ResolutionWidth

We provide a characterization of the resolution width introduced in the context of propositional proof complexity in terms of the existential pebble game introduced in the context of finite model theory. The characterization is tight and purely combinatorial. Our first application of this result is a surprising proof that the minimum space of refuting a 3-CNF formula is always bounded from belo...