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Bisimulation metrics are a successful instrument used to estimate the behavioural distance between probabilistic concurrent systems. They have been defined in both discrete and continuous state space models. However, the weak semantics approach , where non-observable actions are abstracted away, has been adopted only in the discrete case. In this paper we fill this gap and provide a weak bisimulation metric for models with continuous state spaces. A technical difficulty is to provide a suitable notion of weak transition , which requires to lift transitions leaving from states to transitions leaving from a continuous distribution over states. We prove that our weak bisimulation metric is non-expansive , thus allowing for compositional reasoning. We prove that systems at distance zero are equated by a suitable notion of probabilistic weak bisimulation. We apply our theory in a case study where continuous distributions derive from the evolution of the physical environment. [ABSTRACT FROM AUTHOR]

Rule formats are sets of syntactical constraints over SOS rules ensuring semantical properties of the derived LTS. Given a rule format, our proposal is to relax the constraints imposed on each single rule and to introduce some constraints on the form of the whole set of rules, thus obtaining a new format ensuring the same semantical property and being less demanding than the original one. We apply our idea to a well known rule format for rooted branching bisimulation equivalence. [ABSTRACT FROM AUTHOR]

We present Dynamic Hierarchical Machines (DHMs), an extension of Communicating Hierarchical Automata allowing dynamic activation of components. We give an operational semantics of DHMs and we provide examples of modeling in the context of security. We characterize a fragment of DHMs which are equivalent to Recursive Hierarchical Machines and therefore to Pushdown Machines. [ABSTRACT FROM AUTHOR]