Best-fit Interval Extensions of Partially Defined Boolean Functions
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چکیده
Interval functions constitute quite a special class of Boolean functions for which it is very easy and fast to determine their functional value on a specified input vector. Their value is true, if and only if the input data viewed as an n-bit integer belongs to the interval [a, b] corresponding to the function concerned. In this paper we show, that the problem of finding an interval function, which makes the minimum number of errors for a given partially defined Boolean function, is NP-hard, if we do not specify the ordering of variables in advance. In case we have a fixed ordering of variables, it can be solved in polynomial time and we present an asymptotically optimal polynomial time algorithm for this problem.
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تاریخ انتشار 2007