Comparing Reductions to NP-Complete Sets

2006 ◽  
pp. 465-476 ◽  
Author(s):  
John M. Hitchcock ◽  
A. Pavan
Keyword(s):  
Np Complete ◽  
Complete Sets

Unions of Disjoint NP-Complete Sets

2011 ◽  
pp. 240-251
Author(s):  
Christian Glaßer ◽  
John M. Hitchcock ◽  
A. Pavan ◽  
Stephen Travers
Keyword(s):  
Np Complete ◽  
Complete Sets

Relativized isomorphisms of NP-complete sets

1993 ◽  
Vol 3 (2) ◽  
pp. 186-205 ◽  
Author(s):  
Judy Goldsmith ◽  
Deborah Joseph
Keyword(s):  
Np Complete ◽  
Complete Sets

scholarly journals One-way functions and the nonisomorphism of NP-complete sets

1991 ◽  
Vol 81 (1) ◽  
pp. 155-163 ◽  
Author(s):  
Juris Hartmanis ◽  
Lane A. Hemachandra
Keyword(s):  
Np Complete ◽  
Complete Sets

scholarly journals THE INFORMATIONAL CONTENT OF CANONICAL DISJOINT NP-PAIRS

2009 ◽  
Vol 20 (03) ◽  
pp. 501-522 ◽  
Author(s):  
CHRISTIAN GLAßER ◽  
ALAN L. SELMAN ◽  
LIYU ZHANG
Keyword(s):  
Open Problem ◽  
Structural Complexity ◽  
Informational Content ◽  
Proof Systems ◽  
Canonical Pair ◽  
Propositional Proof Systems ◽  
Np Complete ◽  
Complete Sets ◽  
Propositional Proof ◽  
Almost All

We investigate the connection between propositional proof systems and their canonical pairs. It is known that simulations between propositional proof systems translate to reductions between their canonical pairs. We focus on the opposite direction and study the following questions. Q1: For which propositional proof systems f and g does the implication [Formula: see text] hold, and for which does it fail? Q2: For which propositional proof systems of different strengths are the canonical pairs equivalent? Q3: What do (non-)equivalent canonical pairs tell about the corresponding propositional proof systems? Q4: Is every NP-pair (A, B), where A is NP-complete, strongly many-one equivalent to the canonical pair of some propositional proof system? In short, we show that Q1 and Q2 can be answered with 'for almost all', which generalizes previous results by Pudlák and Beyersdorff. Regarding Q3, inequivalent canonical pairs tell that the propositional proof systems are not "very similar," while equivalent, P -inseparable canonical pairs tell that they are not "very different." We can relate Q4 to the open problem in structural complexity that asks whether unions of disjoint NP-complete sets are NP-complete. This demonstrates a new connection between propositional proof systems, disjoint NP-pairs, and unions of disjoint NP-complete sets.

Properties of NP‐Complete Sets

2006 ◽  
Vol 36 (2) ◽  
pp. 516-542 ◽  
Author(s):  
Christian Glaßer ◽  
A. Pavan ◽  
Alan L. Selman ◽  
Samik Sengupta
Keyword(s):  
Np Complete ◽  
Complete Sets

Autoreducibility of NP-Complete Sets under Strong Hypotheses

2017 ◽  
Vol 27 (1) ◽  
pp. 63-97
Author(s):  
John M. Hitchcock ◽  
Hadi Shafei
Keyword(s):  
Np Complete ◽  
Complete Sets
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