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Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
ISBN: 0-7695-0850-2
pp: 251
I. Newman , Dept. of Comput. Sci., Haifa Univ., Israel
ABSTRACT
Combinatorial property testing, initiated formally by (Goldreich et al., 1996) and inspired by (Rubinfeld and Sudan, 1996), deals with the following relaxation of decision problems: given a fixed property and an input x, one wants to decide whether x has the property or is being far from having the property. The main result here is that if G={g:{0,1}/sup n//spl rarr/{0,1}} is a family of Boolean functions that have read-once branching programs of width w, then for every n and /spl epsiv/<0 there is a randomized algorithm that always accepts every x/spl isin/{0,1}/sup n/ if g(x)=1, and rejects it with height probability if at least /spl epsiv/n bits of x should be modified in order for it to be in g/sup -1/(1). The algorithm queries (2w//spl epsiv/)/sup 0(w)/ many queries. In particular, for constant /spl epsiv/ and w, the query complexity is 0(1). This generalizes the results of (Alon et al., 1999) asserting that regular languages are efficiently (/spl epsiv/,O(1))-testable.
INDEX TERMS
randomised algorithms; Boolean functions; probability; computational complexity; directed graphs; small width branching programs; combinatorial property testing; decision problems; Boolean functions; read-once branching programs; randomized algorithm; probability; query complexity; regular languages
CITATION
I. Newman, "Testing of function that have small width branching programs", FOCS, 2000, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2000, pp. 251, doi:10.1109/SFCS.2000.892112
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