Adaptivity Helps for Testing Juntas

Authors Rocco A. Servedio, Li-Yang Tan, John Wright

Thumbnail PDF


  • Filesize: 0.52 MB
  • 16 pages

Document Identifiers

Author Details

Rocco A. Servedio
Li-Yang Tan
John Wright

Cite AsGet BibTex

Rocco A. Servedio, Li-Yang Tan, and John Wright. Adaptivity Helps for Testing Juntas. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 264-279, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


We give a new lower bound on the query complexity of any non-adaptive algorithm for testing whether an unknown Boolean function is a k-junta versus epsilon-far from every k-junta. Our lower bound is that any non-adaptive algorithm must make Omega(( k * log*(k)) / ( epsilon^c * log(log(k)/epsilon^c))) queries for this testing problem, where c is any absolute constant <1. For suitable values of epsilon this is asymptotically larger than the O(k * log(k) + k/epsilon) query complexity of the best known adaptive algorithm [Blais,STOC'09] for testing juntas, and thus the new lower bound shows that adaptive algorithms are more powerful than non-adaptive algorithms for the junta testing problem.
  • Property testing
  • juntas
  • adaptivity


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Noga Alon, Eric Blais, Sourav Chakraborty, David García-Soriano, and Arie Matsliah. Nearly tight bounds for testing function isomorphism. SIAM J. Comput., 42(2):459-493, 2013. Google Scholar
  2. J. Arpe and E. Mossel. Application of a generalization of Russo’s formula to learning from multiple random oracles. Combinatorics, Probability and Computing, 19:183-199, 2010. Google Scholar
  3. J. Arpe and R. Reischuk. Robust inference of relevant attributes. In Proceedings of the Fourteenth International Conference on Algorithmic Learning Theory, pages 99-113, 2003. Google Scholar
  4. A. Atıcı and R. Servedio. Quantum algorithms for testing and learning juntas. Quantum Information Processing, 6(5):323-348, 2007. Google Scholar
  5. M. Ben-Or and N. Linial. Collective coin flipping. In S. Micali, editor, Randomness and Computation, pages 91-115. Academic Press, 1990. Google Scholar
  6. Arthur J. Bernstein. Maximally connected arrays on the n-cube. SIAM J. Appl. Math., 15(6):1485-1489, 1967. Google Scholar
  7. E. Blais. Testing juntas: A brief survey. In Property Testing - Current Research and Surveys, pages 32-40, 2010. Google Scholar
  8. Eric Blais. Improved bounds for testing juntas. In Proc. RANDOM, pages 317-330, 2008. Google Scholar
  9. Eric Blais. Testing juntas nearly optimally. In Proceedings of STOC, pages 151-158, 2009. Google Scholar
  10. Eric Blais, Joshua Brody, and Badih Ghazi. The information complexity of hamming distance. In RANDOM, pages 462-486, 2014. Google Scholar
  11. Eric Blais, Joshua Brody, and Kevin Matulef. Property testing lower bounds via communication complexity. In CCC, pages 210-220, 2011. Google Scholar
  12. Eric Blais and Daniel M. Kane. Tight bounds for testing k-linearity. In RANDOM, pages 435-446, 2012. Google Scholar
  13. Eric Blais and Ryan O'Donnell. Lower bounds for testing function isomorphism. In IEEE Conference on Computational Complexity, pages 235-246, 2010. Google Scholar
  14. Eric Blais, Amit Weinstein, and Yuichi Yoshida. Partially symmetric functions are efficiently isomorphism-testable. In FOCS, pages 551-560, 2012. Google Scholar
  15. A. Blum. Relevant examples and relevant features: Thoughts from computational learning theory. in AAAI Fall Symposium on `Relevance', 1994. Google Scholar
  16. A. Blum and P. Langley. Selection of relevant features and examples in machine learning. Artificial Intelligence, 97(1-2):245-271, 1997. Google Scholar
  17. Harry Buhrman, David García-Soriano, Arie Matsliah, and Ronald de Wolf. The non-adaptive query complexity of testing k-parities. Chicago Journal of Theoretical Computer Science, 2013, 2013. Google Scholar
  18. Sourav Chakraborty, Eldar Fischer, David García-Soriano, and Arie Matsliah. Junto-symmetric functions, hypergraph isomorphism and crunching. In CCC, pages 148-158, 2012. Google Scholar
  19. Sourav Chakraborty, David García-Soriano, and Arie Matsliah. Efficient sample extractors for juntas with applications. In ICALP, pages 545-556. Springer, 2011. Google Scholar
  20. H. Chockler and D. Gutfreund. A lower bound for testing juntas. Information Processing Letters, 90(6):301-305, 2004. Google Scholar
  21. D. Dachman-Soled, V. Feldman, L.-Y. Tan, A. Wan, and K. Wimmer. Approximate resilience, monotonicity, and the complexity of agnostic learning. In SODA, pages 498-511, 2015. Google Scholar
  22. A. Dhagat and L. Hellerstein. PAC learning with irrelevant attributes. In Proceedings of the Thirty-Fifth Annual Symposium on Foundations of Computer Science, pages 64-74, 1994. Google Scholar
  23. I. Diakonikolas, H. Lee, K. Matulef, K. Onak, R. Rubinfeld, R. Servedio, and A. Wan. Testing for concise representations. In Proc. 48th Ann. Symposium on Computer Science (FOCS), pages 549-558, 2007. Google Scholar
  24. I. Diakonikolas, H.K. Lee, K. Matulef, R. Servedio, and A. Wan. Efficiently testing sparse GF(2) polynomials. Algorithmica, 61(3):580-605, 2011. Google Scholar
  25. Vitaly Feldman, Parikshit Gopalan, Subhash Khot, and Ashok Kumar Ponnuswami. On agnostic learning of parities, monomials, and halfspaces. SIAM J. Comput., 39(2):606-645, 2009. Google Scholar
  26. E. Fischer, G. Kindler, D. Ron, S. Safra, and A. Samorodnitsky. Testing juntas. J. Computer & System Sciences, 68(4):753-787, 2004. Google Scholar
  27. Peter Frankl. On the trace of finite sets. J. Comb. Theory, Ser. A, 34(1):41-45, 1983. Google Scholar
  28. O. Goldreich, editor. Property Testing: Current Research and Surveys. Springer, 2010. LNCS 6390. Google Scholar
  29. P. Gopalan, R. O'Donnell, R. Servedio, A. Shpilka, and K. Wimmer. Testing Fourier dimensionality and sparsity. SIAM J. on Computing, 40(4):1075-1100, 2011. Google Scholar
  30. D. Guijarro, J. Tarui, and T. Tsukiji. Finding relevant variables in the PAC model with membership queries. In Proceedings of the Tenth International Conference on Algorithmic Learning Theory, pages 313-322, 1999. Google Scholar
  31. Larry H. Harper. Optimal assignments of numbers to vertices. SIAM J. Appl. Math., 12(1):131-135, 1964. Google Scholar
  32. Sergiu Hart. A note on the edges of the n-cube. Disc. Math., 14:157-163, 1976. Google Scholar
  33. J. H. Lindsey. Assignment of numbers to vertices. Amer. Math. Monthly, 71:508-516, 1964. Google Scholar
  34. K. Matulef, R. O'Donnell, R. Rubinfeld, and R. Servedio. Testing halfspaces. SIAM J. on Comput., 39(5):2004-2047, 2010. Google Scholar
  35. Kevin Matulef, Ryan O'Donnell, Ronitt Rubinfeld, and Rocco A. Servedio. Testing ±1-weight halfspace. In APPROX-RANDOM, pages 646-657, 2009. Google Scholar
  36. Colin McDiarmid. Concentration. In Probabilistic Methods for Algorithmic Discrete Mathematics, pages 195-248, 1998. Google Scholar
  37. E. Mossel, R. O'Donnell, and R. Servedio. Learning functions of k relevant variables. Journal of Computer & System Sciences, 69(3):421-434, 2004. Preliminary version in Proc. STOC'03. Google Scholar
  38. D. Ron. Property Testing: A Learning Theory Perspective. Foundations and Trends in Machine Learning, 1(3):307-402, 2008. Google Scholar
  39. D. Ron. Algorithmic and analysis techniques in property testing. Foundations and Trends in Theoretical Computer Science, 5:73-205, 2010. Google Scholar
  40. D. Ron and R. Servedio. Exponentially improved algorithms and lower bounds for testing signed majorities. In SODA, pages 1319-1336, 2013. Google Scholar
  41. D. Ron and G. Tsur. Testing computability by width-two OBDDs. Theoretical Computer Science, 420:64-79, 2012. Google Scholar
  42. Gregory Valiant. Finding Correlations in Subquadratic Time, with Applications to Learning Parities and Juntas. In FOCS, pages 11-20, 2012. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail