TY - GEN

T1 - Testing for concise representations

AU - Diakonikolas, Ilias

AU - Lee, Homin K.

AU - Matulef, Kevin

AU - Onak, Krzysztof

AU - Rubinfeld, Ronitt

AU - Servedio, Rocco A.

AU - Wan, Andrew

PY - 2007

Y1 - 2007

N2 - We describe a general method for testing whether a function on n input variables has a concise representation. The approach combines ideas from the junta test of Fischer et al. [6] with ideas from learning theory, and yields property testers that make poly(s/t) queries (independent of n) for Boolean function classes such as s-term DNF formulas (answering a question posed by Parnas et al. [12]), size-s decision trees, size-s Boolean formulas, and size-s Boolean circuits. The method can be applied to non-Boolean valued function classes as well. This is achieved via a generalization of the notion of variation from Fischer et al. to non-Boolean functions. Using this generalization we extend the original junta test of Fischer et al. to work for non-Boolean functions, and give poly(s/ε)-query testing algorithms for non-Boolean valued function classes such as size-s algebraic circuits and s-sparse polynomials over finite fields. We also prove an ω̃(√ s) query lower bound for nonadaptively testing s-sparse polynomials over finite fields of constant size. This shows that in some instances, our general method yields a property tester with query complexity that is optimal (for nonadaptive algorithms) up to a polynomial factor.

AB - We describe a general method for testing whether a function on n input variables has a concise representation. The approach combines ideas from the junta test of Fischer et al. [6] with ideas from learning theory, and yields property testers that make poly(s/t) queries (independent of n) for Boolean function classes such as s-term DNF formulas (answering a question posed by Parnas et al. [12]), size-s decision trees, size-s Boolean formulas, and size-s Boolean circuits. The method can be applied to non-Boolean valued function classes as well. This is achieved via a generalization of the notion of variation from Fischer et al. to non-Boolean functions. Using this generalization we extend the original junta test of Fischer et al. to work for non-Boolean functions, and give poly(s/ε)-query testing algorithms for non-Boolean valued function classes such as size-s algebraic circuits and s-sparse polynomials over finite fields. We also prove an ω̃(√ s) query lower bound for nonadaptively testing s-sparse polynomials over finite fields of constant size. This shows that in some instances, our general method yields a property tester with query complexity that is optimal (for nonadaptive algorithms) up to a polynomial factor.

UR - http://www.scopus.com/inward/record.url?scp=46749151826&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2007.4389524

DO - 10.1109/FOCS.2007.4389524

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AN - SCOPUS:46749151826

SN - 0769530109

SN - 9780769530109

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 549

EP - 558

BT - Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007

T2 - 48th Annual Symposium on Foundations of Computer Science, FOCS 2007

Y2 - 20 October 2007 through 23 October 2007

ER -