A new polynomial-time algorithm for linear programming
Combinatorica
Dualization of regular Boolean functions
Discrete Applied Mathematics
An O(mn) algorithm for regular set-covering problems
Theoretical Computer Science
Disjoint products and efficient computation of reliability
Operations Research
An O(nm)-time algorithm for computing the dual of a regular Boolean function
Discrete Applied Mathematics - Special volume: viewpoints on optimization
Polynomial-Time Recognition of 2-Monotonic Positive Boolean Functions Given by an Oracle
SIAM Journal on Computing
The Maximum Latency and Identification of Positive Boolean Functions
SIAM Journal on Computing
A fast and simple algorithm for identifying 2-monotonic positive Boolean functions
Journal of Algorithms
Complexity theoretic hardness results for query learning
Computational Complexity
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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A positive (or monotone) Boolean function is regular if its variables are naturally ordered, left to right, by decreasing strength, so that shifting the nonzero component of any true vector to the left always yields another true vector. This paper considers the problem of recognizing whether a positive function f is regular, where f is given by min T(f) (the set of all minimal true vectors of f). We propose a simple linear time (i.e., O(n|min T(f)|)- time) algorithm for it. This improves upon the previous algorithm by Provan and Ball which requires O(n2|min T(f)|) time. As a corollary, we also present an O(n(n + |min T(f)|))- time algorithm for the recognition problem of 2-monotonic functions.