# Computing the Value of a Boolean Expression with Interval Inputs is NP-Hard

Computing the Value of a Boolean Expression with Interval Inputs is NP-Hard To make an expert system work, we must store the statements that comprise expert knowledge. These statements usually have a degree of uncertainty associated with them, and these degrees of uncertainty are naturally described by intervals (sub-intervals of the interval [0, 1]). When we ask a query that is a logical combination of the statements stored in the system, we must, therefore, use interval computations to compute its resulting degree of certainty. In this paper, we prove that in general, computing these degrees of belief is intractable (NP-hard). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Computing the Value of a Boolean Expression with Interval Inputs is NP-Hard

, Volume 3 (2) – Oct 14, 2004
18 pages

/lp/springer_journal/computing-the-value-of-a-boolean-expression-with-interval-inputs-is-np-n2C60pEgBY
Publisher
Springer Journals
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009937906231
Publisher site
See Article on Publisher Site

### Abstract

To make an expert system work, we must store the statements that comprise expert knowledge. These statements usually have a degree of uncertainty associated with them, and these degrees of uncertainty are naturally described by intervals (sub-intervals of the interval [0, 1]). When we ask a query that is a logical combination of the statements stored in the system, we must, therefore, use interval computations to compute its resulting degree of certainty. In this paper, we prove that in general, computing these degrees of belief is intractable (NP-hard).

### Journal

Reliable ComputingSpringer Journals

Published: Oct 14, 2004

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