CTL and ECTL as fragments of the modal &mgr;-calculus
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
An introduction to distributed algorithms
An introduction to distributed algorithms
Modal logic
Distributed Algorithms
Modal logics for finite graphs
Logic for concurrency and synchronisation
Graph Theory With Applications
Graph Theory With Applications
Modal Expressiveness of Graph Properties
Electronic Notes in Theoretical Computer Science (ENTCS)
On the complexity of hybrid logics with binders
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
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Graphs are among the most frequently used structures in computer science. A lot of problems can be modelled using a graph and can then be solved by checking whether the graph satisfies some property. In this work, we are interested in how to use logical frameworks as a generic tool to express and efficiently check graph properties. In order to reason about this, we choose to analyze the Hamiltonian property and choose the family of modal logics as our framework. Our analysis has to deal with two central issues: whether each of the modal languages under consideration has enough expressive power to describe this property and how complex (computationally) it is to use these logics to actually test whether a given graph has this property. First, we show that this property is not definable in a basic modal logic or in any bisimulation-invariant extension of it, like the modal @m-calculus. We then show that it is possible to express it in a basic hybrid logic. Unfortunately, the Hamiltonian property still cannot be efficiently checked in this logic. In a second attempt, we extend this basic hybrid logic with the @7 operator and show that we can check the Hamiltonian property with optimal (NP-Complete) complexity in this logic.