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On the Randomness Complexity of Property Testing

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2007, RANDOM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4627))

Abstract

We initiate a general study of the randomness complexity of property testing, aimed at reducing the randomness complexity of testers without (significantly) increasing their query complexity. One concrete motivation for this study is provided by the observation that the product of the randomness and query complexity of a tester determine the actual query complexity of implementing a version of this tester that utilizes a weak source of randomness (through a randomness-extractor). We present rather generic upper- and lower-bounds on the randomness complexity of property testing and study in depth the special case of testing bipartiteness in two standard property testing models.

This work is based on the M.Sc. thesis of the second author, which was completed under the supervision of the first author. This research was partially supported by the Israel Science Foundation (grant No. 460/05).

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References

  • Alon, N., Dar, S., Parnas, M., Ron, D.: Testing of Clustering. SIDMA 16(3), 393–417 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Alon, N., Fischer, E., Krivelevich, M., Szegedy, M.: Efficient testing of large graphs. In: 40th FOCS, pp. 645–655 (1999)

    Google Scholar 

  • Alon, N., Fischer, E., Newman, I., Shapira, A.: A Combinatorial Characterization of the Testable Graph Properties: It’s All About Regularity. In: 38th STOC, pp. 251–260 (2006)

    Google Scholar 

  • Alon, N., Krivelevich, M.: Testing k-Colorability. SIDMA 15(2), 211–227 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Ben-Sasson, E., Sudan, M., Vadhan, S., Wigderson, A.: Randomness-efficient low degree tests and short PCPs via epsilon-biased sets. In: Proc. 35th STOC, pp. 612–621 (June 2003)

    Google Scholar 

  • Blum, M., Luby, M., Rubinfeld, R.: Self-testing/correcting with applications to numerical problems. JCSS 47, 549–595 (1993)

    MathSciNet  MATH  Google Scholar 

  • Canetti, R., Even, G., Goldreich, O.: Lower Bounds for Sampling Algorithms for Estimating the Average. IPL 53, 17–25 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • Fischer, E.: The art of uninformed decisions: A primer to property testing. Bulletin of the EATCS 75, 97–126 (2001)

    MathSciNet  MATH  Google Scholar 

  • Goldreich, O.: Another motivation for reducing the randomness complexity of algorithms. Position paper. ECCC (2006)

    Google Scholar 

  • Goldreich, O., Goldwasser, S., Ron, D.: Property testing and its connection to learning and approximation. JACM, 653–750 (July 1998)

    Google Scholar 

  • Goldreich, O., Goldwasser, S., Lehman, E., Ron, D., Samorodnitsky, A.: Testing Monotonicity. Combinatorica 20(3), 301–337 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • Goldreich, O., Ron, D.: Property testing in bounded degree graphs. Algorithmica, 302–343 (2002)

    Google Scholar 

  • Goldreich, O., Ron, D.: A sublinear bipartite tester for bounded degree graphs. Combinatorica 19(3), 335–373 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Goldreich, O., Sudan, M.: Locally testable codes and PCPs of almost linear length. JACM 53(4), 558–655 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Goldreich, O., Trevisan, L.: Three theorems regarding testing graph properties. Random Structures and Algorithms 23(1), 23–57 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Lovász, L., Young, N.: Lecture Notes on Evasiveness of Graph Properties.TR-317-91, Computer Science Dept. Princeton University (1991)

    Google Scholar 

  • Ron, D.: Property testing. In: Handbook on Randomization, pp. 597–649 (2001)

    Google Scholar 

  • Rubinfeld, R., Sudan, M.: Robust characterization of polynomials with applications to program testing. SICOMP 25(2), 252–271 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Shaltiel, R.: Recent Developments in Explicit Constructions of Extractors. Bulletin of the EATCS 77, 67–95 (2002)

    MathSciNet  MATH  Google Scholar 

  • Sheffet, O.: Reducing the Randomness Complexity of Property Testing, with an Emphasis on Testing Bipartiteness. M.Sc. Thesis, Weizmann Institute of Science (December 2006), available from http://www.wisdom.weizmann.ac.il/~oded/p-ors.html

  • Shpilka, A., Wigderson, A.: Derandomizing Homomorphism Testing in General Groups. SICOMP, vol. 36-4, pp.1215–1230, 2006

    Google Scholar 

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Author information

Authors and Affiliations

  1. Weizmann Institute of Science, Rehovot, Israel

    Oded Goldreich & Or Sheffet

Authors
  1. Oded Goldreich
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  2. Or Sheffet
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Editor information

Editors and Affiliations

  1. Computer Science Dept., Princeton University, 35 Olden Street, NJ 08540-5233, Princeton, USA

    Moses Charikar

  2. Institut für Informatik, Christian-Albrechts-Universität zu Kiel,, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Omer Reingold

  4. Centre Universitaire d’Informatique,, Battelle bâtiment A, route de Drize 7, 1227, Geneva, Carouge, Switzerland

    José D. P. Rolim

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© 2007 Springer-Verlag Berlin Heidelberg

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Goldreich, O., Sheffet, O. (2007). On the Randomness Complexity of Property Testing. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_37

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  • DOI: https://doi.org/10.1007/978-3-540-74208-1_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74207-4

  • Online ISBN: 978-3-540-74208-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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