Interval extensions of partially defined Boolean functions

Authors:
Ondřej Čepek;David Kronus;Petr Kučera
Affiliations:
Charles University, Dep. of Theoret. Comp. Science, Prague 1, Czech Republic;Charles University, Dep. of Theoret. Comp. Science, Prague 1, Czech Republic;Charles University, Dep. of Theoret. Comp. Science, Prague 1, Czech Republic
Venue:
ACS'06 Proceedings of the 6th WSEAS international conference on Applied computer science
Year:
2006

Citing 3
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Computing the minimum DNF representation of Boolean functions defined by intervals

Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions

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Abstract

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. The value of an n-variable interval function specified by interval [a, b] (where a and b are n-bit binary numbers) is true if and only if the input vector viewed as an n-bit number belongs to the interval [a, b]. Partially defined Boolean function (pdBf) is a pair (T, F) of sets of vectors representing truepoints and falsepoints respectively. In this paper we study the problem of finding an interval extension of given pdBf, that is a Boolean function f which respects truepoints and falsepoints of the input pdBf and can be represented by an interval. We present a polynomial-time algorithm which solves this problem.