Decision tree approximations of Boolean functions
نویسندگان
چکیده
منابع مشابه
Decision Tree Approximations of Boolean Functions
Decision trees are popular representations of Boolean functions. We show that, given an alternative representation of a Boolean function f , say as a read-once branching program, one can find a decision tree T which approximates f to any desired amount of accuracy. Moreover, the size of the decision tree is at most that of the smallest decision tree which can represent f and this construction c...
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The problem of computing best low order approximations of Boolean functions is treated in this paper. We focus on the case of best quadratic approximations of a wide class of cubic functions of arbitrary number of variables, and provide formulas for their efficient calculation. Our methodology is developed upon Shannon’s expansion formula and properties of best affine approximations of quadrati...
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We consider two probability distributions on Boolean functions defined in terms of their representations by and/or trees (or formulas). The relationships between them, and connections with the complexity of the function, are studied. New and improved bounds on these probabilities are given for a wide class of functions, with special attention being paid to the constant function True and read-on...
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Several logi -based languages, su h as Prolog II and its su essors, SICStus Prolog and Oz, o er a omputation domain in luding rational trees. In nite rational trees allow for inreased expressivity ( y li terms an provide eÆ ient representations of grammars and other useful obje ts) and for faster uni ation (due to the safe omission of the o urshe k). Unfortunately, the use of in nite rational t...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2002
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(01)00011-1