On the complexity of minimizing median normal forms of monotone Boolean functions and lattice polynomials

International audienceIn this document, we consider a median-based calculus to represent monotone Boolean functions efficiently. We study an equa-tional specification of median forms and extend it from the domain of monotone Boolean functions to the domain of polynomial functions over distributive lattices. This specification is sound and complete. We illustrate its usefulness when simplifying median formulas algebraically. Furthermore, we propose a definition of median normal forms (MNF), that are thought of as minimal median formulas with respect to a structural ordering of expressions. We investigate related complexity issues and show that the problem of deciding whether a formula is in MNF, that is the problem of minimizing the median form of a monotone Boolean function, is in Σ P 2. Moreover, we show that it still holds for arbitrary Boolean functions, not necessarily monotone

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum