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Computing Behavioural Relations, Logically
 In Proceedings of 18th International Colloquium on Automata, Languages and Programming
, 1991
"... This paper develops a modelchecking algorithm for a fragment of the modal mucalculus and shows how it may be applied to the efficient computation of behavioral relations between processes. The algorithm's complexity is proportional to the product of the size of the process and the size of the f ..."
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Cited by 28 (7 self)
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This paper develops a modelchecking algorithm for a fragment of the modal mucalculus and shows how it may be applied to the efficient computation of behavioral relations between processes. The algorithm's complexity is proportional to the product of the size of the process and the size of the formula, and thus improves on the best existing algorithm for such a fixed point logic. The method for computing preorders that the model checker induces is also more efficient than known algorithms.
Verification of Temporal and RealTime properties of Statecharts
, 1997
"... We present a compositional approach for the verification of temporal and realtime properties of statecharts. Statecharts is a synchronous language that is obtained by extending classical statetransition diagrams with notions of parallelism, broadcast communication and hierarchy. These features hav ..."
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Cited by 15 (3 self)
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We present a compositional approach for the verification of temporal and realtime properties of statecharts. Statecharts is a synchronous language that is obtained by extending classical statetransition diagrams with notions of parallelism, broadcast communication and hierarchy. These features have been shown to permit very elegant and modular specifications. However, the synchrony hypothesis leads to some drawbacks in the definition of a formal semantics, because of wellknown causal paradoxes.
The first result is the definition of a compositional labelled transition system semantics for statecharts that provides the basis for compositional verification. Such a semantics is obtained by translating statecharts into a new
process language called SP, that is characterized by an operator of process refinement for representing the statecharts hierarchy. We show how to instantiate the basic actions and the operations over actions of SP in order to have processes agreeing with the Pnueli and Shalev semantics of statecharts. We define a compositional proof system for checking whether an SP process satisfies a mucalculus formula. This proof system exploits the technique of tagging fixpoints of Winskel for supporting local model checking. It is proved to be sound in general and complete for finitestate processes, i.e. for statecharts.
Finally, we show how this compositional approach to verification can be adapted to a discrete timed version of statechart by considering an extension of mucalculus with freeze quantification and clock constraints. The main idea is that of considering judgments relativized MOREto clock constraints and of adapting the tagged fixpoints method to
this framework.
A Compositional Proof System for the Modal µCalculus
, 1994
"... We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal µcalculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal µcalculus and com ..."
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Cited by 15 (0 self)
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We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal µcalculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal µcalculus and combines it with techniques from work on local model checking. The proof system is sound for all processes and complete for a class of finitestate processes.
On Model Checking InfiniteState Systems
 In Nerode and Matiyasevich, editors, LFCS'94: Logic at St. Petersburg. Symposium on Logical Foundations of Computer Science
, 1994
"... This paper presents a proof method for proving that infinitestate systems satisfy properties expressed in the modal ¯calculus. The method is sound and complete relative to externally proving inclusions of sets of states. It can be seen as a recast of a tableau method due to Bradfield and Stirling ..."
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Cited by 3 (0 self)
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This paper presents a proof method for proving that infinitestate systems satisfy properties expressed in the modal ¯calculus. The method is sound and complete relative to externally proving inclusions of sets of states. It can be seen as a recast of a tableau method due to Bradfield and Stirling following lines used by Winskel for finitestate systems. Contrary to the tableau method, it avoids the use of constants when unfolding fixed points and it replaces the rather involved global success criterion in the tableau method with local success criteria. A proof tree is now merely a means of keeping track of where possible choices are made  and can be changed  and not an essential ingredient in establishing the correctness of a proof: A proof will be correct when all leaves are directly seen to be valid. Therefore, it seems wellsuited for implementation as a tool, by, for instance, integration into existing generalpurpose theorem provers. 1 Introduction Verifying dynamic propert...
A Polyadic Modal µCalculus
, 1994
"... The propositional µcalculus of Kozen extends modal logic with fixed points to achieve a powerful logic for expressing temporal properties of systems modelled by labelled transition systems. We further extend Kozen's logic with polyadic modalities to allow for expressing also quite naturally behavio ..."
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The propositional µcalculus of Kozen extends modal logic with fixed points to achieve a powerful logic for expressing temporal properties of systems modelled by labelled transition systems. We further extend Kozen's logic with polyadic modalities to allow for expressing also quite naturally behavioural relations like bisimulation equivalence and simulation preorders. We show that the problem of model checking is still efficiently decidable, giving rise to efficient worstcase algorithms for verifying the infinity of behavioural relations expressible in this polyadic modal µcalculus. Some of these algorithms compete in efficiency with carefully handcrafted algorithms found in the literature. In spite of this result, the validity problem turns out to be highly undecidable. This is in contrast to the propositional µcalculus where it is decidable in deterministic exponential time. It follows as a corollary, that  also in contrast to the propositional µcalculus  the polyadic modal...