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Bisimulation and Coverings for Graphs and Hypergraphs

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Logic and Its Applications (ICLA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7750))

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Abstract

We survey notions of bisimulation and of bisimilar coverings both in the world of graph-like structures (Kripke structures, transition systems) and in the world of hypergraph-like general relational structures. The provision of finite analogues for full infinite tree-like unfoldings, in particular, raises interesting combinatorial challenges and is the key to a number of interesting model-theoretic applications.

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References

  1. Alon, N.: Tools from higher algebra. In: Graham, R., Grötschel, M., Lovász (eds.) Handbook of Combinatorics, vol. II, pp. 1749–1783. North-Holland (1995)

    Google Scholar 

  2. Andréka, H., van Benthem, J., Németi, I.: Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic 27, 217–274 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bárány, V., Gottlob, G., Otto, M.: Querying the guarded fragment. Logical Methods in Computer Science (submitted, 2012)

    Google Scholar 

  4. Bárány, V., ten Cate, B., Segoufin, L.: Guarded Negation. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 356–367. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. Journal of the ACM 30, 497–513 (1983)

    Article  MathSciNet  Google Scholar 

  6. Berge, C.: Graphs and Hypergraphs. North-Holland (1973)

    Google Scholar 

  7. Biggs, N.: Cubic graphs with large girth. In: Blum, G., et al. (eds.) Annals of the New York Academy of Sciences, vol. 555, pp. 56–62 (1989)

    Google Scholar 

  8. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (2001)

    Google Scholar 

  9. Dawar, A., Otto, M.: Modal characterisation theorems over special classes of frames. Annals of Pure and Applied Logic 161, 1–42 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Goranko, V., Otto, M.: Model theory of modal logic. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, pp. 249–329. Elsevier (2007)

    Google Scholar 

  11. Grädel, E.: On the restraining power of guards. Journal of Symbolic Logic 64, 1719–1742 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Grädel, E., Hirsch, C., Otto, M.: Back and forth between guarded and modal logics. ACM Transactions on Computational Logics 3, 418–463 (2002)

    Article  Google Scholar 

  13. Grädel, E., Otto, M.: The freedoms of (guarded) bisimulation (in preparation, 2012)

    Google Scholar 

  14. Grädel, E., Walukiewicz, I.: Guarded fixed point logic. In: Proc. LICS 1999, pp. 45–54 (1999)

    Google Scholar 

  15. Herwig, B.: Extending partial isomorphisms on finite structures. Combinatorica 15, 365–371 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hodkinson, I., Otto, M.: Finite conformal hypergraph covers and Gaifman cliques in finite structures. Bulletin of Symbolic Logic 9, 387–405 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. Janin, D., Walukiewicz, I.: On the Expressive Completeness of the Propositional μ-Calculus with Respect to Monadic Second-order Logic. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 263–277. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  18. Otto, M.: Modal and guarded characterisation theorems over finite transition systems. Annals of Pure and Applied Logic 130, 173–205 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Otto, M.: Bisimulation invariance and finite models. In: Colloquium Logicum 2002. Lecture Notes in Logic, pp. 276–298. ASL (2006)

    Google Scholar 

  20. Otto, M.: Avoiding incidental homomorphisms into guarded covers. Technical report no. 2600, TU Darmstadt (2009)

    Google Scholar 

  21. Otto, M.: Model theoretic methods for fragments of FO and special classes of (finite) structures. In: Steinhorn, C., Esparza, J., Michaux, C. (eds.) Finite and Algorithmic Model Theory. LMS Lecture Notes, vol. 379, pp. 271–341. CUP (2011)

    Google Scholar 

  22. Otto, M.: Expressive completeness through logically tractable models. Annals of Pure and Applied Logic (under revision, 2012)

    Google Scholar 

  23. Otto, M.: Highly acyclic groups, hypergraph covers and the guarded fragment. Journal of the ACM 59(1) (2012)

    Google Scholar 

  24. Otto, M.: On groupoids and hypergraphs (unpublished draft, 2012)

    Google Scholar 

  25. Rosati, R.: On the decidability and finite controllability of query processing in databases with incomplete information. In: Proc. PODS 2006, pp. 356–365 (2006)

    Google Scholar 

  26. Rosen, E.: Modal logic over finite structures. Journal of Logic, Language and Information 6, 427–439 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  27. ten Cate, B., Segoufin, L.: Unary negation. In: Proceedings of STACS, pp. 344–355 (2011)

    Google Scholar 

  28. van Benthem, J.: Modal Logic and Classical Logic, Bibliopolis, Napoli (1983)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technische Universität Darmstadt, Germany

    Martin Otto

Authors
  1. Martin Otto
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Editor information

Editors and Affiliations

  1. The Institute of Mathematical Sciences, CIT Campus, 600113, Chennai, India

    Kamal Lodaya

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Otto, M. (2013). Bisimulation and Coverings for Graphs and Hypergraphs. In: Lodaya, K. (eds) Logic and Its Applications. ICLA 2013. Lecture Notes in Computer Science, vol 7750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36039-8_2

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  • DOI: https://doi.org/10.1007/978-3-642-36039-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36038-1

  • Online ISBN: 978-3-642-36039-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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