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The Graph Isomorphism Problem: Its Structural Complexity
Introduction Preliminaries Decision Problems, Search Problems, and Counting Problems NP-Completeness The Classes P and NP Reducibility. Reducing the Construction Problem to the Decision ProblemExpand
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Optimal proof systems imply complete sets for promise classes
TLDR
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
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On pseudorandomness and resource-bounded measure
TLDR
We extend a key result of Nisan and Wigderson (J. Expand
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New Collapse Consequences of NP Having Small Circuits
TLDR
We show that if a self-reducible set has polynomial-size circuits, then it is low for the probabilistic class ZPP(NP). Expand
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New Collapse Consequences of NP Having Small Circuits
TLDR
We show that if a self-reducible set has polynomial-size circuits, then it is low for the probabilistic class ZPP (NP). Expand
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On counting and approximation
TLDR
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
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Completeness results for graph isomorphism
TLDR
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
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Is the Standard Proof System for SAT P-Optimal?
TLDR
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
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The Difference and Truth-Table Hierarchies for NP
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 deuxExpand
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Complexity-Restricted Advice Functions
TLDR
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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