Incremental polynomial time dualization of quadratic functions and a subclass of degree-k functions

We consider the problem of dualizing a Boolean function f represented by a DNF. In its most general form, this problem is commonly believed not to be solvable by a quasi-polynomial total time algorithm. We show that if the input DNF is quadratic or is a special degree- k DNF, then dualization turns...

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Vydáno v:Annals of operations research Ročník 188; číslo 1; s. 251 - 261
Hlavní autor: Karasan, O. Ekin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.08.2011
Springer Science + Business Media
Springer
Springer Nature B.V
Témata:
Algorithms
Artificial intelligence
Boolean
Boolean functions
Business and Management
Codes
Combinatorics
Equivalence
Game theory
Graphs
Operations research
Operations Research/Decision Theory
Studies
Theory of Computation
Japan
Polynomial total time algorithm
Degree
function
Boolean function
Hypergraph transversal
Dualization
Quadratic function
ISSN:0254-5330, 1572-9338
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Shrnutí:We consider the problem of dualizing a Boolean function f represented by a DNF. In its most general form, this problem is commonly believed not to be solvable by a quasi-polynomial total time algorithm. We show that if the input DNF is quadratic or is a special degree- k DNF, then dualization turns out to be equivalent to hypergraph dualization in hypergraphs of bounded degree and hence it can be achieved in incremental polynomial time.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-009-0637-x