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 prove the following results on OBDD approximations of Boolean functions:
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1
We show that OBDDs approximating the well–known hidden weighted bit function for uniformly distributed inputs with constant error have size \(2^{\Theta(n^{1/4})}\), improving a previously known result.
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2
We prove that for every variable order π the approximation of some output bits of integer multiplication with constant error requires π-OBDDs of exponential size.
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Gronemeier, A. (2004). Approximating Boolean Functions by OBDDs. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_17
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DOI: https://doi.org/10.1007/978-3-540-28629-5_17
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