Recognizing Structural Patterns on Graphs for the Efficient Computation of #2SAT

  • Guillermo De Ita
  • Pedro Bello
  • Meliza Contreras
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7914)


To count models for two conjunctive forms (#2SAT problem) is a classic #P problem. We determine different structural patterns on the underlying graph of a 2-CF F allowing the efficient computation of #2SAT(F).

We show that if the constrained graph of a formula is acyclic or the cycles on the graph can be arranged as independent and embedded cycles, then the number of models of F can be counted efficiently.


#SAT Problem Counting models Structural Patterns Graph Topologies 


  1. 1.
    Angelsmark, O., Jonsson, P.: Improved Algorithms for Counting Solutions in Constraint Satisfaction Problems. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 81–95. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Dahllöf, V., Jonsonn, P., Wahlström, M.: Counting models for 2SAT and 3SAT formulae. J. Theoretical Computer Sciences 332(1-3), 265–291 (2005)zbMATHCrossRefGoogle Scholar
  3. 3.
    Darwiche, A.: On the Tractability of Counting Theory Models and its Application to Belief Revision and Truth Maintenance. J. of Applied Non-classical Logics 11(1-2), 11–34 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    De Ita, G., Tovar, M.: Applying Counting Models of Boolean Formulas to Propositional Inference. J. Advances in Computer Science and Engineering Researching in Computing Science 19, 159–170 (2006)Google Scholar
  5. 5.
    De Ita, G., Bello, P., Contreras, M.: New Polynomial Classes for #2SAT Established via Graph-Topological Structure. Engineering Letters 15(2), 250–258 (2007)Google Scholar
  6. 6.
    Dubois, O.: Counting the number of solutions for instances of satisfiability. J. Theoretical Computer Sciences 81(1), 49–64 (1991)zbMATHCrossRefGoogle Scholar
  7. 7.
    Fürer, M., Prasad, S.K.: Algorithms for Counting 2-SAT Solutions and Coloring with Applications. Technical Report No. 33, Electronic Colloqium on Comp. Complexity (2005)Google Scholar
  8. 8.
    Littman, M.L., Pitassi, T., Impagliazzo, R.: On the Complexity of counting satisfying assignments. Technical Report Unpublished manuscriptGoogle Scholar
  9. 9.
    Roth, D.: On the hardness of approximate reasoning. J. Artificial Intelligence 82, 273–302 (1996)CrossRefGoogle Scholar
  10. 10.
    Russ, B.: Randomized Algorithms: Approximation, Generation, and Counting, Distingished dissertations. Springer (2001)Google Scholar
  11. 11.
    Zhang, W.: Number of models and satisfiability of set of clauses. J. Theoretical Computer Sciences 155(1), 277–288 (1996)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Guillermo De Ita
    • 1
  • Pedro Bello
    • 1
  • Meliza Contreras
    • 1
  1. 1.Faculty of Computer ScienceBenemérita Universidad Autónoma de PueblaMéxico

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