Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Rubinfeld, R., Sudan, M.: Robust characterization of polynomials with applications to program testing. SIAM Journal on Computing 25(2), 252–271 (1996)
Goldreich, O., Goldwasser, S., Ron, D.: Property testing and its connection to learning and approximation. Journal of the ACM 45(4), 653–750 (1998)
Parnas, M., Ron, D., Samorodnitsky, A.: Testing basic boolean formulae. SIAM Journal on Discrete Math. 16(1), 20–46 (2002)
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)
Goldreich, O., Ron, D.: Private communications (2009)
Newman, I.: Testing membership in languages that have small width branching programs. SIAM Journal on Computing 31(5), 1557–1570 (2002)
Ergün, F., Kumar, R.S., Rubinfeld, R.: On learning bounded-width branching programs. In: COLT 1995, pp. 361–368 (1995)
Bshouty, N., Tamon, C., Wilson, D.: On learning width two branching programs. Information Processing Letters 65, 217–222 (1998)
Bergadano, F., Bshouty, N., Tamon, C., Varricchio, S.: On learning branching programs and small depth circuits. In: COLT 1997, pp. 150–161 (1997)
RagHavan, V., Wilkins, D.: Learning branching programs with queries. In: COLT 1993, pp. 27–36 (1993)
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)
Nakamura, A.: Query learning of bounded-width OBDDs. Theoretical Computer Science 241, 83–114 (2000)
Nakamura, A.: An efficient query learning algorithm for OBDDs. Information and Computation 201, 178–198 (2005)
Ron, D., Tsur, G.: Testing computability by width two obdds where the variable order is unknown (2010), http://www.eng.tau.ac.il/~danar
Blum, M., Luby, M., Rubinfeld, R.: Self-testing/correcting with applications to numerical problems. Journal of the ACM 47, 549–595 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ron, D., Tsur, G. (2010). Testing Computability by Width-2 OBDDs Where the Variable Order is Unknown. In: Calamoneri, T., Diaz, J. (eds) Algorithms and Complexity. CIAC 2010. Lecture Notes in Computer Science, vol 6078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13073-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-13073-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13072-4
Online ISBN: 978-3-642-13073-1
eBook Packages: Computer ScienceComputer Science (R0)