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Using modal logics to express and check global graph properties

M. R. F. Benevides, L. M. Schechter
2009 Logic Journal of the IGPL  
Second, we express a necessary and sufficient condition for the Eulerian property to hold using a graded modal logic.  ...  This involves two issues: whether each of the modal languages under consideration has enough expressive power to describe these properties and how complex (computationally) it is to use these logics to  ...  In this work, we analyze how we can express and efficiently check these global graph properties with modal logics.  ... 
doi:10.1093/jigpal/jzp021 fatcat:u5i4wueo3vcmndb5nibo7mbgny

A Logical Approach to Hamiltonian Graphs

L. Menasché Schechter
2009 Electronical Notes in Theoretical Computer Science  
In this work, we are interested in how to use logical frameworks as a generic tool to express and efficiently check graph properties.  ...  use these logics to actually test whether a given graph has this property.  ...  The works presented in [5] and [6] are closely related to this one. In [5] , the interest was also in how to use modal logics to express global graph properties.  ... 
doi:10.1016/j.entcs.2009.07.052 fatcat:wxh46l2pb5betbqos3stkbcqhq

Hybrid Logics and NP Graph Properties [chapter]

Francicleber Martins Ferreira, Cibele Matos Freire, Mario R. F. Benevides, L. Menasché Schechter, Ana Teresa Martins
2011 Lecture Notes in Computer Science  
These results lead to the definition of syntactically defined fragments of hybrid logic whose model checking problem is complete for each degree in the polynomial hierarchy.  ...  We show that for each property of graphs G in NP there is a sequence φ 1 , φ 2 , . . . of formulas of the full hybrid logic which are satisfied exactly by the frames in G.  ...  Hybrid Modal logics have low expressive power, hence we do not aim to associate to each graph property a single formula.  ... 
doi:10.1007/978-3-642-20920-8_15 fatcat:665g5saazfew3flvcaackknim4

Procedure-modular specification and verification of temporal safety properties

Siavash Soleimanifard, Dilian Gurov, Marieke Huisman
2013 Journal of Software and Systems Modeling  
Both linear-time temporal logic and finite automata are supported as formalisms for expressing local and global safety properties, allowing the user to choose a suitable format for the property at hand  ...  This approach allows global properties to be verified in the presence of code evolution, multiple method implementations (as arising from software product lines), or even unknown method implementations  ...  implementation of cvpp and ProMoVer, and to Stefan Schwoon for adapting the input language of Moped to our needs.  ... 
doi:10.1007/s10270-013-0321-0 fatcat:lmko3khlnvgh3o6el2pcz26h7y

Procedure-modular verification of control flow safety properties

Siavash Soleimanifard, Dilian Gurov, Marieke Huisman
2010 Proceedings of the 12th Workshop on Formal Techniques for Java-Like Programs - FTFJP '10  
Modularity of verification is achieved by relativizing the correctness of global properties on the local properties rather than on the implementations of methods, and is based on the construction of maximal  ...  This paper describes a novel technique for fully automated procedure-modular verification of Java programs equipped with method-local and global assertions that specify safety properties of sequences of  ...  We are indebted to Wojciech Mostowski and Erik Poll for their help in finding a suitable case study, and to Stefan Schwoon for adapting the input language of the PDS model checker Moped to our needs.  ... 
doi:10.1145/1924520.1924525 dblp:conf/ecoop/SoleimanifardGH10 fatcat:5xepdvldjjc4dpmcttvhffi6e4

Abstraction of Graph Transformation Systems by Temporal Logic and Its Verification [chapter]

Mitsuharu Yamamoto, Yoshinori Tanabe, Koichi Takahashi, Masami Hagiya
2008 Lecture Notes in Computer Science  
Acknowledgments The authors are grateful to anonymous reviewers for their constructive comments.  ...  Science and Technology Agency (JST).  ...  Such situations can be naturally expressed by using inverse modalities in temporal logics.  ... 
doi:10.1007/978-3-540-69149-5_57 fatcat:hadfulpoaba4heq3bhfzgcqeou

Polynomial hierarchy graph properties in hybrid logic

F.M. Ferreira, C.M. Freire, M.R.F. Benevides, L. Menasché Schechter, A.T. Martins
2014 Journal of computer and system sciences (Print)  
These results lead to the definition of syntactically defined fragments of hybrid logic whose model checking problem is complete for each degree in the polynomial hierarchy.  ...  In this article, we show that for each property of graphs G in the Polynomial Hierarchy (PH) there is a sequence φ 1 , φ 2 , . . . of formulas of the full hybrid logic which are satisfied exactly by the  ...  Acknowledgements We would like to thank the anonymous referee for its detailed comments and suggestions.  ... 
doi:10.1016/j.jcss.2014.04.003 fatcat:knqjit3fzvdgnkkrjcvotukywe

ProMoVer: Modular Verification of Temporal Safety Properties [chapter]

Siavash Soleimanifard, Dilian Gurov, Marieke Huisman
2011 Lecture Notes in Computer Science  
This approach allows global properties to be verified in the presence of code evolution, multiple method implementations (as arising from software product lines), or even unknown method implementations  ...  This paper describes ProMoVer, a tool for fully automated procedure-modular verification of Java programs equipped with methodlocal and global assertions that specify safety properties of sequences of  ...  , and to Stefan Schwoon for adapting the input language of Moped to our needs.  ... 
doi:10.1007/978-3-642-24690-6_25 fatcat:7h3ee6xc6zcz3f44hbwihj5r7u

Symbolic Model Checking of Tense Logics on Rational Kripke Models [chapter]

Wilmari Bekker, Valentin Goranko
2009 Lecture Notes in Computer Science  
We introduce the class of rational Kripke models and study symbolic model checking of the basic tense logic Kt and some extensions of it on that class.  ...  We show that every formula of Kt has an effectively computable rational extension in every rational Kripke model, and therefore local model checking and global model checking of Kt in rational Kripke models  ...  We use them in Section 5 to show decidability of global and local symbolic model checking of K t in rational Kripke models and in Section 6 we discuss its complexity.  ... 
doi:10.1007/978-3-642-03092-5_2 fatcat:meg6lzhf4baohjbvf337o5nld4

A Modal Logic for π-Calculus and Model Checking Algorithm

Taolue Chen, Tingting Han, Jian Lu
2005 Electronical Notes in Theoretical Computer Science  
In this paper, we use symbolic transition graph inherited from π-calculus to model concurrent systems.  ...  Temporal logic is thought as a good compromise between description convenience and abstraction and can support useful computational applications, such as model-checking.  ...  In [1] [4] and more recently [6] , Amadio and Dam introduced recursion into the modal logic via fixpoints, as in the propositional µ-calculus, thus has the ability to express properties for processes  ... 
doi:10.1016/j.entcs.2004.04.043 fatcat:hid5sshvznhcremcynnfnw6zuu

Modal Expressiveness of Graph Properties

Mario R.F. Benevides, L. Menasché Schechter
2008 Electronical Notes in Theoretical Computer Science  
Finally, we introduce a promising way of expressing properties related to edges and use it to express the Eulerian property.  ...  In this work, we analyze how we can express some important graph properties such as connectivity, acyclicity and the Eulerian and Hamiltonian properties in a modal logic.  ...  [4] is a work closely related to this one. In that work, the interest was also in how to use modal logics to express "global" graph properties.  ... 
doi:10.1016/j.entcs.2008.03.064 fatcat:tbkt73k6nvhh5ph4xrjzkc2fre

Symbolic model checking of tense logics on rational Kripke models [article]

Wilmari Bekker, Valentin Goranko
2008 arXiv   pre-print
We introduce the class of rational Kripke models and study symbolic model checking of the basic tense logic Kt and some extensions of it in models from that class.  ...  We show that every formula of Kt has an effectively computable regular extension in every rational Kripke model, and therefore local model checking and global model checking of Kt in rational Kripke models  ...  We wish to thank Arnaud Carayol, Balder ten Cate, Carlos Areces, Christophe Morvan, and Stéphane Demri, for various useful comments and suggestions.  ... 
arXiv:0810.5516v1 fatcat:gnpsz54nnve5zh6ztcid3kmpxa

Compositional verification of sequential programs with procedures

Dilian Gurov, Marieke Huisman, Christoph Sprenger
2008 Information and Computation  
We present a novel maximal model construction for the fragment of the modal -calculus with boxes and greatest fixed points only, and adapt it to control-flow graphs modelling components described in a  ...  The application of the method involves three steps: (1) decomposing the desired global property into local properties of the components, (2) proving the correctness of the property decomposition by using  ...  The logic we employ to express such properties is a modal logic with box modalities and simultaneous greatest fixed points (written in equational form), which is expressively equivalent to the fragment  ... 
doi:10.1016/j.ic.2008.03.003 fatcat:i2bb4ckl5ngp3aa6ezxzhpqt4a

1 Modal logic: a semantic perspective [chapter]

Patrick Blackburn, Johan van Benthem
2007 Studies in Logic and Practical Reasoning  
But modal logic is not the only tool for talking about graphs, and this brings us to one of the major themes of the chapter: the relationship between modal logic and other forms of logic.  ...  This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames.  ...  And we can immediately use this bridge to transfer results for first-order logic to modal logic. Proof. Suppose the Löwenheim-Skolem property fails.  ... 
doi:10.1016/s1570-2464(07)80004-8 fatcat:unpkk66lxjdibjbv4epdapt6yu

Checking Absence of Illicit Applet Interactions: A Case Study [chapter]

Marieke Huisman, Dilian Gurov, Christoph Sprenger, Gennady Chugunov
2004 Lecture Notes in Computer Science  
Later, when loading applets on a card, the implementations are matched against these local properties, in order to guarantee the global property.  ...  The correctness of a global system property can algorithmically be inferred from local applet properties.  ...  This allows structural properties expressed in temporal logics to be checked using standard model checking tools such as CWB [9] .  ... 
doi:10.1007/978-3-540-24721-0_6 fatcat:try4mxpj2nftlj4dilcqqxpjsi
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