Recognition of interval Boolean functions

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 number belongs to the interval [a, b] corresponding to the function concerned. Therefore we study the problem of deciding whether given DNF represents interval function and if so then we also want to output the corresponding interval. For general Boolean functions this is co-NP-hard. In our article we present a polynomial algorithm which works for monotone functions. We shall also show that given Boolean function f belonging to some class C which is closed under partial assignment and for which we are able to solve the satisfiability problem in polynomial time, we can decide whether f is an interval function in polynomial time.

• Type: Journal
• Year: 2008
• Where: AMAI
• Authors: Ondrej Cepek, David Kronus, Petr Kucera
• Keywords: AMAI 2008, Artificial Intelligence, Boolean Function, Interval Function, Special Class