The Minimal Logically-Defined NP-Complete Problem

Régis Barbanchon (1) , Etienne Grandjean (2)

1 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
2 Equipe AMACC - Laboratoire GREYC - UMR6072

We present an NP complete defined by an existential monadic second order formula over functional structures that : 1 is minimal under several syntactic criteria 2 is unique for such restrictions, up to renamings and symmetries ; our reductions and proofs are surprisingly very elementary and simple in comparison with some recent similar results classifying existential second-order formulas over relational structures according to their ability either to express NP complete problems only PTIME ones

Domaines: Algorithme et structure de données [cs.DS]

Régis Barbanchon, Etienne Grandjean. The Minimal Logically-Defined NP-Complete Problem. Lecture Notes in Computer Science, 2004, pp.338-349. ⟨hal-00255837⟩