Communications of the ACM
On one criterion of the optimality of an algorithm for evaluating monotonic Boolean functions
USSR Computational Mathematics and Mathematical Physics
Predicting Cause-Effect Relationships from Incomplete Discrete Observations
SIAM Journal on Discrete Mathematics
Interactive learning of monotone Boolean functions
Information Sciences: an International Journal
Polynomial-Time Recognition of 2-Monotonic Positive Boolean Functions Given by an Oracle
SIAM Journal on Computing
The reliability issue of computer-aided breast cancer diagnosis
Computers and Biomedical Research
A Fast and Simple Algorithm for Identifying 2-Monotonic Positive Boolean Functions
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
Minimizing the Average Query Complexity of Learning Monotone Boolean Functions
INFORMS Journal on Computing
Data mining and knowledge discovery: a guided approach based on monotone boolean functions
Data mining and knowledge discovery: a guided approach based on monotone boolean functions
The arrowsmith project: 2005 status report
DS'05 Proceedings of the 8th international conference on Discovery Science
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This paper addresses the problem of minimizing the average query complexity of inferring a pair of nested monotone Boolean functions defined on {0, 1}n using a pair of oracles. Here, nested refers to the case when one of the functions is always greater than or equal to the other function. It is shown that the nested case is equivalent to inferring the single function case defined on {0, 1}n+1 when access to the two oracles is unrestricted. Two common examples of restricted oracles, namely sequential oracles and a single three-valued oracle, are also analyzed. The most efficient known approach to minimizing the average query complexity in inferring a single monotone Boolean function is based on a query selection criterion. It is shown that the selection criterion approach is easily modified for use with restricted oracles. Several real world examples illustrate the necessity and sufficiency of the nested monotone Boolean function model. Extensive computational results indicate that the nestedness assumption reduces the average query complexity by a few percent. This is a dramatic improvement considering the fact that this complexity is exponential in n.