Introduction Preliminaries Decision Problems, Search Problems, and Counting Problems NP-Completeness The Classes P and NP Reducibility. Reducing the Construction Problem to the Decision Problem… Expand

We show a close connection between the existence of (p-)optimal proof systems and complete problems for certain promise complexity classes like UP, NP ∩ Sparse, RP or BPP and prove that C has a many-one complete set if and only if C is a proof system with a p-optimal test set.Expand

We introduce a new class of functions, called span functions which count the different output values that occur at the leaves of the computation tree associated with a nondeterministic polynomial time Turing machine transducer.Expand

We prove that the graph isomorphism problem restricted to trees and to colored graphs with color multiplicities 2 and 3 is many-one complete for several complexity classes within NC2.Expand

We investigate the question whether there is a (p-)optimal proof system for SAT or for TAUT and its relation to completeness and collapse results for nondeterministic function classes.Expand

Definition de deux hierarchies des classes de complexite. Localisation de la hierarchie de differences et de la hierarchie du tableau de verite pour NP. Exemples d'ensembles complets dans les deux… Expand

The authors consider uniform subclasses of the nonuniform complexity classes defined by Karp and Lipton [L'Enseign. Comput. System Sci., 38 (1989), pp. 511--523] via the notion of advice functions.Expand