• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • LAMSADE (UMR CNRS 7243)
  • LAMSADE : Publications
  • View Item
  •   BIRD Home
  • LAMSADE (UMR CNRS 7243)
  • LAMSADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - No thumbnail

Locally monotone Boolean and pseudo-Boolean functions

Waldhauser, Tamás; Marichal, Jean-Luc; Couceiro, Miguel (2012), Locally monotone Boolean and pseudo-Boolean functions, Discrete Applied Mathematics, 160, 12, p. 1651-1660. http://dx.doi.org/10.1016/j.dam.2012.03.006

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1107.1161
Date
2012
Journal name
Discrete Applied Mathematics
Volume
160
Number
12
Publisher
Elsevier
Pages
1651-1660
Publication identifier
http://dx.doi.org/10.1016/j.dam.2012.03.006
Metadata
Show full item record
Author(s)
Waldhauser, Tamás
Marichal, Jean-Luc
Couceiro, Miguel
Abstract (EN)
We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if none of its partial derivatives changes in sign on tuples which differ in less than p positions. As it turns out, this parameterized notion provides a hierarchy of monotonicities for pseudo-Boolean (Boolean) functions. Local monotonicities are shown to be tightly related to lattice counterparts of classical partial derivatives via the notion of permutable derivatives. More precisely, p-locally monotone functions are shown to have p-permutable lattice derivatives and, in the case of symmetric functions, these two notions coincide. We provide further results relating these two notions, and present a classification of p-locally monotone functions, as well as of functions having p-permutable derivatives, in terms of certain forbidden “sections”, i.e., functions which can be obtained by substituting constants for variables. This description is made explicit in the special case when p=2.
Subjects / Keywords
Boolean function; pseudo-Boolean function; local monotonicity; discrete partial derivative; join and meet derivatives

Related items

Showing items related by title and author.

  • Thumbnail
    Hierarchies of local monotonicities and lattice derivatives for Boolean and pseudo-Boolean functions 
    Waldhauser, Tamás; Marichal, Jean-Luc; Couceiro, Miguel (2012) Communication / Conférence
  • Thumbnail
    Axiomatizations of quasi-Lovász extensions of pseudo-Boolean functions 
    Marichal, Jean-Luc; Couceiro, Miguel (2011) Article accepté pour publication ou publié
  • Thumbnail
    Axiomatizations of Lovász extensions of pseudo-Boolean functions 
    Marichal, Jean-Luc; Couceiro, Miguel (2012-09-27) Article accepté pour publication ou publié
  • Thumbnail
    An algorithm for producing median normal form representations for Boolean functions 
    Waldhauser, Tamás; Marichal, Jean-Luc; Lehtonen, Erkko; Couceiro, Miguel (2011) Communication / Conférence
  • Thumbnail
    The arity gap of order-preserving functions and extensions of pseudo-Boolean functions 
    Waldhauser, Tamás; Lehtonen, Erkko; Couceiro, Miguel (2012) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo