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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 characterising the state-based metric is much simpler than an earlier logic by Desharnais et al. as it uses only two non-expansive operators rather than the general class of non-expansive operators.
Many behavioural equivalences or preorders for probabilistic processes involve a lifting operation that turns a relation on states into a relation on distributions of states. We show that several existing proposals for lifting relations can be reconc
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial structures, such as
We propose a process calculus, named AbC, to study the behavioural theory of interactions in collective-adaptive systems by relying on attribute-based communication. An AbC system consists of a set of parallel components each of which is equipped wit
Let $X$, $Y$ be sets and let $Phi$, $Psi$ be mappings with the domains $X^{2}$ and $Y^{2}$ respectively. We say that $Phi$ is combinatorially similar to $Psi$ if there are bijections $f colon Phi(X^2) to Psi(Y^{2})$ and $g colon Y to X$ such that $Ps
This paper studies the quantitative refinements of Abramskys applicative similarity and bisimilarity in the context of a generalisation of Fuzz, a call-by-value $lambda$-calculus with a linear type system that can express programs sensitivity, enrich