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On the Relationship between Spatial Logics and Behavioral Simulations

  • Lucia Acciai
  • Michele Boreale
  • Gianluigi Zavattaro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6014)

Abstract

Spatial logics have been introduced to reason about distributed computation in models for concurrency. We first define a spatial logic for a general class of infinite-state transition systems, the Spatial Transition Systems (sts), where a monoidal structure on states accounts for the spatial dimension. We then show that the model checking problem for this logic is undecidable already when interpreted over Petri nets. Next, building on work by Finkel and Schnöbelen, we introduce a subclass of sts, the Well-Structured sts (ws-sts), which is general enough to include such models as Petri nets, Broadcast Protocols, ccs and Weighted Automata. Over ws-sts, an interesting fragment of spatial logic - the monotone fragment - turns out to be decidable under reasonable effectiveness assumptions. For this class of systems, we also offer a Hennessy-Milner theorem, characterizing the logical preorder induced by the monotone fragment as the largest spatial-behavioural simulation. We finally prove that, differently from the corresponding logic, this preorder is in general not decidable, even when confining to effective ws-sts.

Keywords

Monoidal Structure Model Check Problem Broadcast Protocol Concrete Instance Behavioral Simulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Lucia Acciai
    • 1
  • Michele Boreale
    • 1
  • Gianluigi Zavattaro
    • 2
  1. 1.Dipartimento di Sistemi e InformaticaUniversità di FirenzeItaly
  2. 2.Dipartimento di Scienze dell’InformazioneUniversità di BolognaItaly

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