Stochastic Boolean Function Evaluation (SBFE) is the problem of determining
the value of a given Boolean function
f on an unknown input
x, when each
bit of
of
x can only be determined by paying a given associated cost
. Further,
x is drawn from a given product distribution: for each
,
, and the bits are independent. The goal is to minimize the
expected
... [Show full abstract] cost of evaluation. Stochastic Boolean Function Evaluation (SBFE) is
the problem of determining the value of a given Boolean function f on an
unknown input x, when each bit of of x can only be determined by
paying a given associated cost . Further, x is drawn from a given
product distribution: for each , , and the bits are
independent. The goal is to minimize the expected cost of evaluation. In this
paper, we study the complexity of the SBFE problem for classes of DNF formulas.
We consider both exact and approximate versions of the problem for subclasses
of DNF, for arbitrary costs and product distributions, and for unit costs
and/or the uniform distribution.