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41st Annual Symposium on Foundations of Computer Science
Testing of function that have small width branching programs
Redondo Beach, California
November 12-November 14
ISBN: 0-7695-0850-2
I. Newman, Dept. of Comput. Sci., Haifa Univ., Israel
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
I. Newman, "Testing of function that have small width branching programs," focs, pp.251, 41st Annual Symposium on Foundations of Computer Science, 2000
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