Dualization of regular Boolean functions
Discrete Applied Mathematics
The complexity of Boolean functions
The complexity of Boolean functions
On generating all maximal independent sets
Information Processing Letters
Disjoint products and efficient computation of reliability
Operations Research
Cause-effect relationships and partially defined Boolean functions
Annals of Operations Research
Computational learning theory: an introduction
Computational learning theory: an introduction
An O(nm)-time algorithm for computing the dual of a regular Boolean function
Discrete Applied Mathematics - Special volume: viewpoints on optimization
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
Complexity of identification and dualization of positive Boolean functions
Information and Computation
Interior and exterior functions of Boolean functions
Discrete Applied Mathematics
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
The Maximum Latency and Identification of Positive Boolean Functions
SIAM Journal on Computing
Error-free and best-fit extensions of partially defined Boolean functions
Information and Computation
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Dual-Bounded Generating Problems: Partial and Multiple Transversals of a Hypergraph
SIAM Journal on Computing
Deductive inference for the interiors and exteriors of horn theories
ACM Transactions on Computational Logic (TOCL)
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The interior and exterior functions of a Boolean function f were introduced in Makino and Ibaraki (Discrete Appl. Math. 69 (1996) 209-231), as stability (or robustness) measures of the f. In this paper, we investigate the complexity of two problems α-INTERIOR and α-EXTERIOR, introduced therein. We first answer the question about the complexity of α-INTERIOR left open in Makino and Ibaraki (Discrete Appl. Math. 69 (1996) 209-231); it has no polynomial total time algorithm even if α is bounded by a constant, unless P = NP. However, for positive h-term DNF functions with h bounded by a constant, problems α-INTERIOR and α-EXTERIOR can be solved in (input) polynomial time and polynomial delay, respectively. Furthermore, for positive k-DNF functions, α-INTERIOR for two cases in which k = 1, and α and k are both bounded by a constant, can be solved in polynomial delay and in polynomial time, respectively.