Abstract
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 = (f n ) 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 (n 1/4).
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Bollig, B. (2005). Property Testing and the Branching Program Size of Boolean Functions. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_23
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DOI: https://doi.org/10.1007/11537311_23
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