Approximating Boolean functions by OBDDs

Authors:
Andre Gronemeier
Affiliations:
Lehrstuhl Informatik 2, Universität Dortmund, Germany
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

In learning theory and genetic programming, OBDDs are used to represent approximations of Boolean functions. This motivates the investigation of the OBDD complexity of approximating Boolean functions with respect to given distributions on the inputs. We present a new type of reduction for one-round communication problems that is suitable for approximations. Using this new type of reduction, we improve a known lower bound on the size of OBDD approximations of the hidden weighted bit function for uniformly distributed inputs to an asymptotically tight bound and prove new results about OBDD approximations of integer multiplication and squaring for uniformly distributed inputs.