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The art of uninformed decisions: A primer to property testing
 Science
, 2001
"... Property testing is a new field in computational theory, that deals with the information that can be deduced from the input where the number of allowable queries (reads from the input) is significally smaller than its size. ..."
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Cited by 131 (21 self)
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Property testing is a new field in computational theory, that deals with the information that can be deduced from the input where the number of allowable queries (reads from the input) is significally smaller than its size.
Quantum testers for hidden group properties
 FUNDAMENTA INFORMATICAE 1–16
, 2008
"... We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the c ..."
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Cited by 9 (1 self)
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We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the common coset range property of two functions having identical ranges within each coset of some normal subgroup. Our periodicity tester is efficient in Abelian groups and generalizes, in several aspects, previous periodicity testers. This is achieved by introducing a technique refining the majority correction process widely used for proving robustness of algebraic properties. The periodicity tester in nonAbelian groups and the common coset range tester are query efficient.
Multilinearity selftesting with relative error
 In Proc. 17th STACS, LNCS 1770
, 2000
"... Abstract. We investigate selftesting programs with relative error by allowing error terms proportional to the function to be computed. Until now, in numerical computation, error terms were assumed to be either constant or proportional to the pth power of the magnitude of the input, for p ∈ [0, 1). ..."
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Cited by 3 (1 self)
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Abstract. We investigate selftesting programs with relative error by allowing error terms proportional to the function to be computed. Until now, in numerical computation, error terms were assumed to be either constant or proportional to the pth power of the magnitude of the input, for p ∈ [0, 1). We construct new selftesters with relative error for realvalued multilinear functions defined over finite rational domains. The existence of such selftesters positively solves an open question in [KMS99]. Moreover, our selftesters are very efficient: they use few queries and simple operations.
Quantum property testing of group solvability
 In Proceedings of 8th LATIN
, 2008
"... Abstract. Testing efficiently whether a finite set Γ with a binary operation · over it, given as an oracle, is a group is a wellknown open problem in the field of property testing. Recently, Friedl, Ivanyos and Santha have made a significant step in the direction of solving this problem by showing ..."
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Cited by 3 (0 self)
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Abstract. Testing efficiently whether a finite set Γ with a binary operation · over it, given as an oracle, is a group is a wellknown open problem in the field of property testing. Recently, Friedl, Ivanyos and Santha have made a significant step in the direction of solving this problem by showing that it it possible to test efficiently whether the input (Γ, ·) is an Abelian group or is far, with respect to some distance, from any Abelian group. In this paper, we make a step further and construct an efficient quantum algorithm that tests whether (Γ, ·) is a solvable group, or is far from any solvable group. More precisely, the number of queries used by our algorithm is polylogarithmic in the size of the set Γ. 1