Paper Info
Title
Is the Standard Proof System for SAT P-Optimal?
Abstract
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. A p-optimal proof system for SAT is shown to imply (1) that there exists a complete function for the class of all total nondeterministic multi-valued functions and (2) that any set with an optimal proof system has a p-optimal proof system. By replacingthe assumption of the mere existence of a (p-) optimal proof system by the assumption that certain proof systems are (p-)optimal we obtain stronger consequences, namely collapse results for various function classes. Especially we investigate the question whether the standard proof system for SAT is p-optimal. We show that this assumption is equivalent to a variety of complexity theoretical assertions studied before, and to the assumption that every optimal proof system is p-optimal. Finally, we investigate whether there is an optimal proof system for TAUT that admits an effective interpolation, and show some relations between various completeness assumptions.
Year
DOI
Venue
2000
10.1007/3-540-44450-5_29
FSTTCS
Keywords
Field
DocType
optimal proof system,sat p-optimal,nondeterministic function class,various completeness assumption,p-optimal proof system,various function class,total nondeterministic multi-valued function,replacingthe assumption,certain proof system,standard proof system,complete function,value function
Analytic proof,Discrete mathematics,Combinatorics,Existential quantification,Nondeterministic algorithm,Turing machine,Proof complexity,Time complexity,Completeness (statistics),Mathematics,Direct proof
Conference
Volume
ISSN
ISBN
1974
0302-9743
3-540-41413-4
Citations 
PageRank 
References 
10
0.63
18
Authors
2
Name
Order
Citations
PageRank
Johannes Köbler158046.51
Jochen Messner2704.86