Guided inference of nested monotone Boolean functions

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 show...

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Vydáno v:Information sciences Ročník 151; s. 171 - 200
Hlavní autoři: Torvik, Vetle I, Triantaphyllou, Evangelos
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.05.2003
Témata:
Average query complexity
Guided inference
Membership queries
Nested monotone Boolean functions
Partially ordered sets (posets)
Query selection criteria
Guided inference
Membership queries
Nested monotone Boolean functions
Average query complexity
Partially ordered sets (posets)
Query selection criteria
ISSN:0020-0255, 1872-6291
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Shrnutí: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.
Bibliografie:ObjectType-Article-2
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ISSN:0020-0255
1872-6291
DOI:10.1016/S0020-0255(03)00062-8