Theory of Computing Systems

, Volume 61, Issue 3, pp 755–776 | Cite as

On Oblivious Branching Programs with Bounded Repetition that Cannot Efficiently Compute CNFs of Bounded Treewidth

  • Igor RazgonEmail author


In this paper we study complexity of an extension of ordered binary decision diagrams (OBDDs) called c-OBDDs on CNFs of bounded (primal graph) treewidth. In particular, we show that for each k ≥ 3 there is a class of CNFs of treewidth k for which the equivalent c-OBDDs are of size Ω(n k/(8c−4)). Moreover, this lower bound holds if c-OBDDs are non-deterministic and semantic. Our second result uses the above lower bound to separate the above model from sentential decision diagrams (SDDs). In order to obtain the lower bound, we use a structural graph parameter called matching width. Our third result shows that matching width and pathwidth are linearly related.


Bipartite Graph Vertex Cover Primal Graph Binary Decision Diagram Graph Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Ablayev, F.M., Khadiev, K.R.: Extension of the hierarchy for k-obdds of small width. Russ. Math. Surv. 57(3), 46–50 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Alon, N., Maass, W.: Meanders and their applications in lower bounds arguments. J. Comput. Syst. Sci. 37(2), 118–129 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bollig, B., Sauerhoff, M., Sieling, D., Wegener, I.: Hierarchy theorems for kobdds and kibdds. Theor. Comput. Sci. 205(1-2), 45–60 (1998)CrossRefzbMATHGoogle Scholar
  4. 4.
    Borodin, A., Razborov, A.A., Smolensky, R.: On lower bounds for read-k-times branching programs. Comput. Complex. 3, 1–18 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bova, S., Capelli, F., Mengel, S., Slivovsky, F.: Expander cnfs have exponential DNNF size. CoRR, arXiv:1411.1995 (2014)
  6. 6.
    Darwiche, A.: SDD: A new canonical representation of propositional knowledge bases. In IJCAI, 819–826 (2011)Google Scholar
  7. 7.
    Ellis, J., Warren, R.: Lower bounds on the pathwidth of some grid-like graphs. Discret. Appl. Math. 156(5), 545–555 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ferrara, A., Pan, G., Vardi, M.Y.: Treewidth in verification Local vs. global. In: LPAR, pp 489–503 (2005)Google Scholar
  9. 9.
    Jukna, S.: Boolean Function Complexity: Advances and frontiers. Springer-Verlag (2012)Google Scholar
  10. 10.
    Khadiev, K.: Width hierarchy for $,k$-obdd of small width. Electronic Colloquium on Computational Complexity (ECCC) 22, 48 (2015)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Krause, M.: Lower bounds for depth-restricted branching programs. Inf. Comput. 91(1), 1–14 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Razgon, I.: No small nondeterministic read-once branching programs for cnfs of bounded treewidth. In IPEC, 319–331 (2014)Google Scholar
  13. 13.
    Razgon, I.: On OBDDs for CNFs of bounded treewidth. In: In Principles of Knowledge Representation and Reasoning (KR) (2014)Google Scholar
  14. 14.
    Razgon, I: Two types of branching programs with bounded repetition that cannot efficiently compute monotone 3-cnfs. CoRR, abs/1510., 05486 (2015)Google Scholar
  15. 15.
    Razgon, I: On the read-once property of branching programs and cnfs of bounded treewidth. Algorithmica 75(2), 277–294 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Vatshelle, M.: New width parameters of graphs. PhD thesis, Department of informatics university of bergen (2012)Google Scholar
  17. 17.
    Wegener, I.: Branching programs and binary decision diagrams. SIAM (2000)Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Computer Science and Information SystemsBirkbeck, University of LondonLondonUK

Personalised recommendations