The Application of the Inclusion-Exclusion Principle in Learning Monotonic Boolean Functions

The IUP Journal of Computer Sciences, Vol. VI, No. 1, January 2012, pp. 39-56

Posted: 20 Sep 2012

See all articles by Thomas Quint

Thomas Quint

University of Nevada-Reno, Department of Mathematics

Christopher Gaffney

Rutgers, The State University of New Jersey - Rutgers University, New Brunswick/Piscataway

Date Written: January 20, 2012

Abstract

In this paper, we consider the inference problem for monotone Boolean structure functions (for example, Torvik and Triantaphyllou, 2002 and 2005; or Judson et al., 2005). We follow Judson’s algorithm (in Judson, 1999; or Judson et al., 2005), except with two possible changes. First, when choosing a vector to test, we consider simply evaluating the “value” of a given number of random vectors (instead of using Judson’s “neighbor” algorithm to find test vectors). Second, we consider a new way of calculating the value of a vector, which makes use of the inclusionexclusion principle from combinatorics. Via testing on some 10-component systems, we find that the “random” approach is better than the “neighbor” approach, and that the inclusionexclusion method is an improvement whenever the size of the boundary of the “unknown vector set” is small.

Keywords: Reliability theory, Semi-coherent structure function, Inclusion-exclusion principle, Inference problem

Suggested Citation

Quint, Thomas and Gaffney, Christopher, The Application of the Inclusion-Exclusion Principle in Learning Monotonic Boolean Functions (January 20, 2012). The IUP Journal of Computer Sciences, Vol. VI, No. 1, January 2012, pp. 39-56, Available at SSRN: https://ssrn.com/abstract=2149383

Thomas Quint (Contact Author)

University of Nevada-Reno, Department of Mathematics ( email )

1664 North Virginia
Reno, NV 89557
United States
775-784-1366 (Phone)
775-784-6378 (Fax)

Christopher Gaffney

Rutgers, The State University of New Jersey - Rutgers University, New Brunswick/Piscataway ( email )

94 Rockafeller Road
New Brunswick, NJ 08901
United States

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