J. Köbler

Publications
Influence

The Graph Isomorphism Problem: Its Structural Complexity

J. Köbler, U. Schöning, J. Torán
Mathematics
1 July 1993

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

Optimal proof systems imply complete sets for promise classes

J. Köbler, J. Messner, J. Torán
Mathematics, Computer Science
Inf. Comput.
10 July 2003

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

On pseudorandomness and resource-bounded measure

V. Arvind, J. Köbler
Mathematics, Computer Science
Theor. Comput. Sci.
28 March 2001

We extend a key result of Nisan and Wigderson (J. Expand

New Collapse Consequences of NP Having Small Circuits

J. Köbler, O. Watanabe
Mathematics, Computer Science
ICALP
10 July 1995

We show that if a self-reducible set has polynomial-size circuits, then it is low for the probabilistic class ZPP(NP). Expand

New Collapse Consequences of NP Having Small Circuits

J. Köbler, O. Watanabe
Mathematics, Computer Science
SIAM J. Comput.
1 February 1999

We show that if a self-reducible set has polynomial-size circuits, then it is low for the probabilistic class ZPP (NP). Expand

On counting and approximation

J. Köbler, U. Schöning, J. Torán
Computer Science
Acta Informatica
2004

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

Completeness results for graph isomorphism

B. Jenner, J. Köbler, P. McKenzie, J. Torán
Mathematics, Computer Science
J. Comput. Syst. Sci.
1 May 2003

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

Is the Standard Proof System for SAT P-Optimal?

J. Köbler, J. Messner
Mathematics, Computer Science
FSTTCS
13 December 2000

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

The Difference and Truth-Table Hierarchies for NP

J. Köbler, U. Schöning, K. Wagner
Mathematics, Computer Science
RAIRO Theor. Informatics Appl.
1987

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

Complexity-Restricted Advice Functions

J. Köbler, T. Thierauf
Mathematics, Computer Science
SIAM J. Comput.
1 April 1994

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

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