ISA 1991: ISA'91 Algorithms pp 104-115

# Identifying 2-monotonic positive boolean functions in polynomial time

• E. Boros
• P. L. Hammer
• T. Ibaraki
• K. Kawakami
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 557)

## Abstract

We consider to identify an unknown Boolean function f by asking an oracle the functional values f(a) for a selected set of test vectors a ε {0,1}n. If f is known to be a positive function of n variables, the algorithm by Gainanov can achieve the goal by issuing O(mn) queries, where m = ¦minT(f)¦ + ¦maxF(f)¦ and minT(f) (resp. maxF(f)) denotes the set of minimal true vectors (resp. maximal false vectors) of f. However, it is not known whether this whole task including the generation of test vectors can be carried out in polynomial time in n and m or not. To partially answer this question, we propose here two algorithms that, given an unknown positive function f of n variables, decide whether f is 2-monotonic or not, and if f is 2-monotonic, output sets min T(f) and max F(f). The first algorithm uses O(nm2+n2m) time and O(nm) queries while the second one uses O(n3m) time and O(n3m) queries.

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## Authors and Affiliations

• E. Boros
• 1
• P. L. Hammer
• 1
• T. Ibaraki
• 2
• K. Kawakami
• 2
1. 1.RUTCOR-Rutgers Center for Operations Research, Bush CampusRutgers UniversityNew BrunswickUSA
2. 2.Department of Applied Mathematics and Physics, Faculty of EngineeringKyoto UniversityKyotoJapan