Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Regular Languages are Testable with a Constant Number of Queries
SIAM Journal on Computing
Testing Membership in Languages that Have Small Width Branching Programs
SIAM Journal on Computing
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Some 3CNF properties are hard to test
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Functions that have read-once branching programs of quadratic size are not necessarily testable
Information Processing Letters
On the strength of comparisons in property testing
Information and Computation
Functions that have read-twice constant width branching programs are not necessarily testable
Random Structures & Algorithms
The difficulty of testing for isomorphism against a graph that is given in advance
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Every monotone graph property is testable
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Testing versus estimation of graph properties
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
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Combinatorial property testing, initiated formally by Goldreich, Goldwasser, and Ron (1998) and inspired by Rubinfeld and Sudan (1996), deals with the relaxation of decision problems. Given a property P the aim is to decide whether a given input satisfies the property P or is far from having the property. For a family of boolean functions f = (fn) the associated property is the set of 1-inputs of f. Newman (2002) has proved that properties characterized by oblivious read-once branching programs of constant width are testable, i.e., a number of queries that is independent of the input size is sufficient. We show that Newman's result cannot be generalized to oblivious read-once branching programs of almost linear size. Moreover, we present a property identified by restricted oblivious read-twice branching programs of constant width and by CNFs with a linear number of clauses, where almost all clauses have constant length, but for which the query complexity is Ω (n1/4).