Testing Computability by Width-2 OBDDs Where the Variable Order is Unknown

  • Dana Ron
  • Gilad Tsur
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6078)


Property testing is concerned with deciding whether an object (e.g. a graph or a function) has a certain property or is “far” (for a prespecified distance measure) from every object with that property. In this work we design and analyze an algorithm for testing functions for the property of being computable by a read-once width-2 Ordered Binary Decision Diagram (OBDD), also known as a branching program, where the order of the variables is not known to us. That is, we must accept a function f if there exists an order of the variables according to which a width-2 OBDD can compute f. The query complexity of our algorithm is \(\tilde{O}({\rm log n}){\rm poly}(1/\epsilon)\). In previous work (in Proceedings of RANDOM, 2009) we designed an algorithm for testing computability by an OBDD with a fixed order, which is known to the algorithm. Thus, we extend our knowledge concerning testing of functions that are characterized by their computability using simple computation devices and in the process gain some insight concerning these devices.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rubinfeld, R., Sudan, M.: Robust characterization of polynomials with applications to program testing. SIAM Journal on Computing 25(2), 252–271 (1996)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Goldreich, O., Goldwasser, S., Ron, D.: Property testing and its connection to learning and approximation. Journal of the ACM 45(4), 653–750 (1998)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Parnas, M., Ron, D., Samorodnitsky, A.: Testing basic boolean formulae. SIAM Journal on Discrete Math. 16(1), 20–46 (2002)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Ron, D., Tsur, G.: Testing computability by width two OBDDs. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. LNCS, vol. 5687, pp. 686–699. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Goldreich, O., Ron, D.: Private communications (2009)Google Scholar
  6. 6.
    Newman, I.: Testing membership in languages that have small width branching programs. SIAM Journal on Computing 31(5), 1557–1570 (2002)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Ergün, F., Kumar, R.S., Rubinfeld, R.: On learning bounded-width branching programs. In: COLT 1995, pp. 361–368 (1995)Google Scholar
  8. 8.
    Bshouty, N., Tamon, C., Wilson, D.: On learning width two branching programs. Information Processing Letters 65, 217–222 (1998)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Bergadano, F., Bshouty, N., Tamon, C., Varricchio, S.: On learning branching programs and small depth circuits. In: COLT 1997, pp. 150–161 (1997)Google Scholar
  10. 10.
    RagHavan, V., Wilkins, D.: Learning branching programs with queries. In: COLT 1993, pp. 27–36 (1993)Google Scholar
  11. 11.
    Gavalda, R., Guijarro, D.: Learning ordered binary decision diagrams. In: Zeugmann, T., Shinohara, T., Jantke, K.P. (eds.) ALT 1995. LNCS, vol. 997, pp. 228–238. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  12. 12.
    Nakamura, A.: Query learning of bounded-width OBDDs. Theoretical Computer Science 241, 83–114 (2000)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Nakamura, A.: An efficient query learning algorithm for OBDDs. Information and Computation 201, 178–198 (2005)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Ron, D., Tsur, G.: Testing computability by width two obdds where the variable order is unknown (2010), http://www.eng.tau.ac.il/~danar
  15. 15.
    Blum, M., Luby, M., Rubinfeld, R.: Self-testing/correcting with applications to numerical problems. Journal of the ACM 47, 549–595 (1993)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dana Ron
    • 1
  • Gilad Tsur
    • 1
  1. 1.School of Electrical EngineeringTel Aviv UniversityTel AvivIsrael

Personalised recommendations