On connected Boolean functions
TL;DR: The relationships between the Boolean hypercube properties and the DNF representations of the associated Boolean functions are studied.
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About: This article is published in Discrete Applied Mathematics. The article was published on 15 Oct 1999. and is currently open access. The article focuses on the topics: Boolean expression & Parity function.
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Citations
The minimum equivalent DNF problem and shortest implicants
Christopher Umans
- 08 Nov 1998
TL;DR: It is proved that the Minimum Equivalent DNF problem is /spl Sigma//sub 2//sup p/-complete, resolving a conjecture due to L.J. Stockmeyer (1976), namely, that of finding the shortest implicant of a Boolean function.
82
Convexity and Logical Analysis of Data
TL;DR: The problem of uniqueness is studied, and a polynomial algorithm is provided for checking whether all $k$-convex extensions agree in a point outside the given data set, which is doubly exponential for small data sets and PAC-learnable for large.
23
•Proceedings Article
Probabilistic classifiers and the concepts they recognize
Manfred Jaeger
- 21 Aug 2003
TL;DR: Every linearly separable concept can be recognized by a naive Bayesian classifier, and it is shown that the expressivity of classifiers on the different levels in the hierarchy is characterized algebraically by separability with polynomials of different degrees.
On the Boolean connectivity problem for Horn relations
TL;DR: It is shown that there exists a set S of Horn relations such that the connectivity problem for S is coNP-complete, and a tractable aspect of Horn and dual Horn relations with respect to characteristic sets is investigated.
19
An Efficient Method for Reliability Analysis of Systems Under Epistemic Uncertainty Using Belief Function Theory
TL;DR: An efficient method based on the inclusion-exclusion principle to compute the reliability of systems in the presence of epistemic uncertainty is presented and it is implied that the bounding interval of the system's reliability can be obtained with two simple calculations using methods similar to those of classical probabilistic approaches.
18
References
•Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
Michael Randolph Garey,David S. Johnson +1 more
- 01 Jan 1979
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
A Way to Simplify Truth Functions
TL;DR: In this paper, a way to simplify truth functions is proposed. But it is difficult to verify the correctness of truth functions and it is not easy to find the truth functions in practice.
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