Logical foundations of artificial intelligence
Logical foundations of artificial intelligence
Information Processing Letters
Error-free and best-fit extensions of partially defined Boolean functions
Information and Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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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Interval functions constitute 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]. In this paper we study the problem of deciding whether a given disjunctive normal form represents an interval function and if so then we also want to output the corresponding interval. For general Boolean functions this problem is co-NP-hard. In our article we present a polynomial time algorithm which works for monotone functions. We shall also show that given a Boolean function f belonging to some class ${\cal C}$ which is closed under partial assignment and for which we are able to solve the satisfiability problem in polynomial time, we can also decide whether f is an interval function in polynomial time. We show how to recognize a "renamable" variant of interval functions, i.e., their variable complementation closure. Another studied problem is the problem of finding an interval extension of partially defined Boolean functions. We also study some other properties of interval functions.