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Register a new userOn Characterising Distributability
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Added by
Rob J. van Glabbeek
Publication date
2013
fields
Informatics Engineering
and research's language is
English
Authors
Rob J. van Glabbeek
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We formalise a general concept of distributed systems as sequential components interacting asynchronously. We define a corresponding class of Petri nets, called LSGA nets, and precisely characterise those system specifications which can be implemented as LSGA nets up to branching ST-bisimilarity with explicit divergence.
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Modern society is dependent on distributed software systems and to verify them different modelling languages such as mobile ambients were developed. To analyse the quality of mobile ambients as a good foundational model for distributed computation, we analyse the level of synchronisation between distributed components that they can express. Therefore, we rely on earlier established synchronisation patterns. It turns out that mobile ambients are not fully distributed, because they can express enough synchronisation to express a synchronisation pattern called M. However, they can express strictly less synchronisation than the standard pi-calculus. For this reason, we can show that there is no good and distributability-preserving encoding from the standard pi-calculus into mobile ambients and also no such encoding from mobile ambients into the join-calculus, i.e., the expressive power of mobile ambients is in between these languages. Finally, we discuss how these results can be used to obtain a fully distributed variant of mobile ambients.
In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for various simulation-like preorders over finite-state processes without divergence. In addition, we show that even without the fixpoint operators this probabilistic mu-calculus can be used to characterise these behavioural relations in the sense that two states are equivalent if and only if they satisfy the same set of formulae.
We provide a characterisation of strong bisimilarity in a fragment of CCS that contains only prefix, parallel composition, synchronisation and a limited form of replication. The characterisation is not an axiomatisation, but is instead presented as a rewriting system. We discuss how our method allows us to derive a new congruence result in the $pi$-calculus: congruence holds in the sub-calculus that does not include restriction nor sum, and features a limited form of replication. We have not formalised the latter result in all details.
In 1992 Wang & Larsen extended the may- and must preorders of De Nicola and Hennessy to processes featuring probabilistic as well as nondeterministic choice. They concluded with two problems that have remained open throughout the years, namely to find complete axiomatisations and alternative characterisations for these preorders. This paper solves both problems for finite processes with silent moves. It characterises the may preorder in terms of simulation, and the must preorder in terms of failure simulation. It also gives a characterisation of both preorders using a modal logic. Finally it axiomatises both preorders over a probabilistic version of CSP.
We study the construction of quasimorphisms on groups acting on trees introduced by Monod and Shalom, that we call median quasimorphisms, and in particular we fully characterise actions on trees that give rise to non-trivial median quasimorphisms. Roughly speaking, either the action is highly transitive on geodesics, it fixes a point in the boundary, or there exists an infinite family of non-trivial median quasimorphisms. In particular, in the last case the second bounded cohomology of the group is infinite dimensional as a vector space. As an application, we show that a cocompact lattice in a product of trees only has trivial quasimorphisms if and only if both closures of the projections on the two factors are locally $infty$-transitive.
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