Abstract
Motivated by a study of Zimand (22nd CCC, 2007), we consider the average-case complexity of property testing (focusing, for clarity, on testing properties of Boolean strings). We make two observations:
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1
In the context of average-case analysis with respect to the uniform distribution (on all strings of a fixed length), property testing is trivial. Specifically, either the yes-instances (i.e., instances having the property) or the no-instances (i.e., instances that are far from having the property) are exponentially rare, and thus the tester may just reject (resp., accept) obliviously of the input.
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2
Turning to average-case derandomization with respect to distributions that assigns noticeable probability mass to both yes-instances and no-instances, we identify a natural class of distributions and testers for which average-case derandomization results can be obtained directly (i.e., without using randomness extractors). Furthermore, the resulting deterministic algorithm may preserve the non-adaptivity of the original tester. (In contrast, Zimand’s argument utilizes a strong type of randomness extractors and introduces adaptivity into the testing process.)
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References
Alon, N.: Testing subgraphs of large graphs. Random Structures and Algorithms 21, 359–370 (2002)
Alon, N., Spencer, J.H.: The Probabilistic Method, 2nd edn. John Wiley & Sons, Inc., Chichester (2000)
Ergun, F., Kannan, S., Kumar, S.R., Rubinfeld, R., Viswanathan, M.: Spot-Checkers. In: 30th STOC, pp. 259–268 (1998)
Even, S., Selman, A.L., Yacobi, Y.: The Complexity of Promise Problems with Applications to Public-Key Cryptography. Inform. and Control 61, 159–173 (1984)
Frieze, A., Kanan, R.: Quick approximation to matrices and applications. Combinatorica 19(2), 175–220 (1999)
Goldreich, O.: A Brief Introduction to Property Testing. In: Goldreich, O., et al. (eds.) Studies in Complexity and Cryptography. LNCS, vol. 6650, pp. 467–471. Springer, Heidelberg (2011)
Goldreich, O., Goldwasser, S., Lehman, E., Ron, D., Samorodnitsky, A.: Testing Monotonicity. Combinatorica 20(3), 301–337 (2000)
Goldreich, O., Goldwasser, S., Ron, D.: Property testing and its connection to learning and approximation. Journal of the ACM, 653–750 (July 1998)
Goldreich, O., Kaufman, T.: Proximity Oblivious Testing and the Role of Invariances. ECCC, TR10-058
Goldreich, O., Ron, D.: Property testing in bounded degree graphs. Algorithmica, 302–343 (2002)
Goldreich, O., Ron, D.: A sublinear bipartite tester for bounded degree graphs. Combinatorica 19(3), 335–373 (1999)
Goldreich, O., Sheffet, O.: On the randomness complexity of property testing. Computational Complexity 19(1), 99–133 (2010); Extended abstract in Proc. of RANDOM 2007 (2007)
Goldreich, O., Trevisan, L.: Three theorems regarding testing graph properties. Random Structures and Algorithms 23(1), 23–57 (2003)
Goldreich, O., Wigderson, A.: Derandomization that is rarely wrong from short advice that is typically good. In: Rolim, J.D.P., Vadhan, S.P. (eds.) RANDOM 2002. LNCS, vol. 2483, pp. 209–223. Springer, Heidelberg (2002)
Kaufman, T., Sudan, M.: Algebraic Property Testing: The Role of Invariances. In: 40th STOC, pp. 403–412 (2008)
Ron, D.: Algorithmic and Analysis Techniques in Property Testing. Foundations and Trends in TCS 5(2), 73–205 (2010)
Rubinfeld, R., Sudan, M.: Robust characterization of polynomials with applications to program testing. SIAM Journal on Computing 25(2), 252–271 (1996)
Zimand, M.: On derandomizing probabilistic sublinear-time algorithms. In: The Proc. of the 22nd IEEE Conference on Computational Complexity, pp. 1–9 (2007)
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Goldreich, O. (2011). On the Average-Case Complexity of Property Testing. In: Goldreich, O. (eds) Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science, vol 6650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22670-0_15
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DOI: https://doi.org/10.1007/978-3-642-22670-0_15
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