On the fractional chromatic number of monotone self-dual Boolean functions

Authors:
Daya Ram Gaur;Kazuhisa Makino
Affiliations:
University of Lethbridge, Lethbridge, AB, Canada;Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan
Venue:
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Year:
2007

Citing 17
Cited 0

How to assign votes in a distributed system

Journal of the ACM (JACM)
Dualization of regular Boolean functions

Discrete Applied Mathematics
Quorum structures in distributed systems

Quorum structures in distributed systems
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
On the complexity of dualization of monotone disjunctive normal forms

Journal of Algorithms
The availability of crumbling wall quorum systems

Discrete Applied Mathematics
The Maximum Latency and Identification of Positive Boolean Functions

SIAM Journal on Computing
Efficient Read-Restricted Monotone CNF/DNF Dualization by Learning with Membership Queries

Machine Learning
A Theory of Coteries: Mutual Exclusion in Distributed Systems

IEEE Transactions on Parallel and Distributed Systems
New Results on Monotone Dualization and Generating Hypergraph Transversals

SIAM Journal on Computing
Efficient dualization of O(log n)-term monotone disjunctive normal forms

Discrete Applied Mathematics
Monotone boolean dualization is in co-NP[log2n]

Information Processing Letters
NP-Completeness: A Retrospective

ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Hypergraph Transversal Computation and Related Problems in Logic and AI

JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Satisfiability and self-duality of monotone boolean functions

Satisfiability and self-duality of monotone boolean functions

Quantified Score

Hi-index	0.00

Visualization

Abstract

We compute the exact fractional chromatic number for several classes of monotone self-dual Boolean functions. We characterize monotone self-dual Boolean functions in terms of the optimal value of a LP relaxation of a suitable strengthening of the standard IP formulation for the chromatic number.We also show that determining the self-duality of monotone Boolean function is equivalent to determining feasibility of a certain point in a polytope defined implicitly.