Skip to main content
SpringerLink
Log in

Hypergraphs in Model Checking: Acyclicity and Hypertree-Width versus Clique-Width

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

Included in the following conference series:

Abstract

The principal aim of model checking is to provide efficient decision procedures for the evaluation of certain logical formulae over finite relational structures. Graphs and hypergraphs are important examples of such structures. If no restrictions are imposed on the logical formulae and on the structures under consideration, then this problem of model checking has a very high computational complexity. Hence, several restrictions have been proposed in the literature on the logical formulae and/or on the structures under consideration, in order to guarantee the tractability of this decision problem, e.g.: acyclicity, bounded tree-width, query-width and hypertree-width in case of queries as well as bounded tree-width and clique-width in case of structures. In this paper, we provide a detailed comparison of the expressive power of these restrictions.

This work was supported by the Austrian Science Fund (FWF) Project N.Z29-INF.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Abiteboul, R. Hull, V. Vianu. Foundations of Databases, Addison-Wesley Publishing Company (1995).

    Google Scholar 

  2. W. Bibel. Constraint Satisfaction from a Deductive Viewpoint. In Artificial Intelligence, Vol 35, pp. 401–413 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  3. H.L. Bodlaender. A linear-time algorithm for finding tree-decompositions of small treewidth. In SIAM Journal on Computing, Vol 25, No 6, pp. 1305–1317 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  4. H.L. Bodlaender. Treewidth: Algorithmic Techniques and Results. In Proc. of MFCS’97, LNCS 1295, pp. 19–36, Springer, (1997).

    Google Scholar 

  5. A.K. Chandra, P.M. Merlin. Optimal Implementation of Conjunctive Queries in Relational Databases. In Proc. of STOC’77, pp. 77–90, ACM Press (1977).

    Google Scholar 

  6. E.M. Clarke, O. Grumberg, D. Peled. Model Checking, MIT Press (1999).

    Google Scholar 

  7. Ch. Chekuri, A. Rajaraman. Conjunctive Query Containment Revisited. In Proc. of ICDT’97, LNCS 1186, pp. 130–144, Springer (1997).

    Google Scholar 

  8. D.G. Corneil, M. Habib, J.-M. Langlinel, B. Reed, U. Rotics. Polynomial Time Recognition of clique-width ≤ 3 graphs, extended abstract. In Proc. of LATIN 2000, LNCS 1776, pp. 126–134, Springer (2000).

    Chapter  Google Scholar 

  9. B. Courcelle. Graph Rewriting: An Algebraic and Logic Approach. In Handbook of Theoretical Computer Science, Vol 2, pp. 194–241, J. van Leeuwen (ed.), Elsevier Science Publishers (1990).

    Google Scholar 

  10. B. Courcelle. Monadic second-order logic of graphs VII: Graphs as relational structures. In Theoretical Computer Science, Vol 101, pp. 3–33 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Courcelle, J. Engelfriet, G. Rozenberg. Handle-rewriting hypergraph grammars. In Journal of Computer and System Sciences, Vol 46, pp. 218–270 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  12. B. Courcelle, J.A. Makowsky, U. Rotics. Linear time solvable optimization problems on graphs of bounded clique-width. In Theory of Computing Systems, Vol 33, pp. 125–150 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  13. B. Courcelle, S. Olariu. Upper bounds on the clique-width of graphs. In Discrete Applied Mathematics, Vol 101, pp. 77–114 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  14. A. D’Atri, M. Moscarini. Acyclic Hypergraphs: Their recognition and top-down versus bottom-up generation. Technical Report R.29, Consiglio Nazionale delle Ricerche, Istituto di Analisi dei Sistemi ed Informatica (1982).

    Google Scholar 

  15. R.G. Downey, M.R. Fellows. Parameterized Complexity, Springer-Verlag (1997).

    Google Scholar 

  16. R. Fagin. Degrees of Acyclicity for Hypergraphs and Relational Database Schemes. In Journal of the ACM, Vol 30, No 3, pp. 514–550 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  17. J. Flum, M. Frick, and M. Grohe. Query Evaluation via Tree-Decomposition. In Proc. of ICDT’01. Currently available at http://www.math.uic.edu/grohe/pub/query.ps

  18. G. Gottlob, N. Leone, F. Scarcello. The Complexity of Acyclic Conjunctive Queries. In Proc. of FOCS’98, pp. 706–715, (1998). Full paper to appear in JACM.

    Google Scholar 

  19. G. Gottlob, N. Leone, F. Scarcello. Hypertree Decompositions and Tractable Queries. In Proc. of PODS’99, pp. 21–32, ACM Press (1999).

    Google Scholar 

  20. G. Gottlob, N. Leone, F. Scarcello. A Comparison of Structural CSP Decomposition Methods. In Proc. of IJCAI’99, pp. 394–399, Morgan Kaufmann, (1999).

    Google Scholar 

  21. G. Gottlob, R. Pichler. Hypergraphs in Model Checking: Acyclicity and Hypertree-Width versus Clique-Width. Full paper. Available from the authors (2001).

    Google Scholar 

  22. M. Grohe, T. Schwentick, and L. Segoufin. When is the Evaluation of Conjunctive Queries Tractable Manuscript, currently available at: http://www.math.uic.edu/grohe/ pub/grid.ps (2001).

  23. Ph.G. Kolaitis and M.Y. Vardi. Conjunctive-Query Containment and Constraint Satisfaction. In Proc. of PODS’98, pp. 205–213, ACM Press (1998).

    Google Scholar 

  24. K. Kunen: Answer Sets and Negation as Failure. In Proc. of the Fourth Int. Conf. on Logic Programming, Melbourne, pp. 219–228 (1987).

    Google Scholar 

  25. M. Yannakakis. Algorithms for Acyclic Database Schemes. In Proc. of Int. Conf. on Very Large Data Bases (VLDB’81), pp. 82–94, Cannes, France (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Wien, Austria

    Georg Gottlob

  2. Technische Universität Wien, Austria

    Reinhard Pichler

Authors
  1. Georg Gottlob
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reinhard Pichler
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gottlob, G., Pichler, R. (2001). Hypergraphs in Model Checking: Acyclicity and Hypertree-Width versus Clique-Width. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_58

Download citation

  • DOI: https://doi.org/10.1007/3-540-48224-5_58

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation