scholarly journals Survey of polynomial transformations between NP-complete problems

2011 ◽  
Vol 235 (16) ◽  
pp. 4851-4865 ◽  
Author(s):  
Jorge A. Ruiz-Vanoye ◽  
Joaquín Pérez-Ortega ◽  
Rodolfo A. Pazos R. ◽  
Ocotlán Díaz-Parra ◽  
Juan Frausto-Solís ◽  
...  
Keyword(s):  
Complete Problems ◽  
Polynomial Transformations ◽  
Np Complete

Application of formal languages in polynomial transformations of instances between NP-complete problems

2013 ◽  
Vol 14 (8) ◽  
pp. 623-633
Author(s):  
Jorge A. Ruiz-Vanoye ◽  
Joaquín Pérez-Ortega ◽  
Rodolfo A. Pazos Rangel ◽  
Ocotlán Díaz-Parra ◽  
Héctor J. Fraire-Huacuja ◽  
...  
Keyword(s):  
Formal Languages ◽  
Complete Problems ◽  
Polynomial Transformations ◽  
Np Complete

NP vs QMA_\log(2)

2010 ◽  
Vol 10 (1&2) ◽  
pp. 141-151
Author(s):  
S. Beigi
Keyword(s):  
Quantum Algorithms ◽  
Np Hard ◽  
Complete Problems ◽  
Hard Problems ◽  
Np Complete ◽  
Np Hard Problems

Although it is believed unlikely that $\NP$-hard problems admit efficient quantum algorithms, it has been shown that a quantum verifier can solve NP-complete problems given a "short" quantum proof; more precisely, NP\subseteq QMA_{\log}(2) where QMA_{\log}(2) denotes the class of quantum Merlin-Arthur games in which there are two unentangled provers who send two logarithmic size quantum witnesses to the verifier. The inclusion NP\subseteq QMA_{\log}(2) has been proved by Blier and Tapp by stating a quantum Merlin-Arthur protocol for 3-coloring with perfect completeness and gap 1/24n^6. Moreover, Aaronson et al. have shown the above inclusion with a constant gap by considering $\widetilde{O}(\sqrt{n})$ witnesses of logarithmic size. However, we still do not know if QMA_{\log}(2) with a constant gap contains NP. In this paper, we show that 3-SAT admits a QMA_{\log}(2) protocol with the gap 1/n^{3+\epsilon}} for every constant \epsilon>0.

scholarly journals NP-complete problems for systems of divisibilities of values of linear polynomials

2017 ◽  
Vol 4(62) (2) ◽  
pp. 236-246
Author(s):  
Nikolay K. Kosovskii ◽  
◽  
Tatiana M. Kosovskaya ◽  
Nikolay N. Kosovskii ◽  
Mikhail R. Starchak ◽  
...  
Keyword(s):  
Complete Problems ◽  
Np Complete ◽  
Linear Polynomials

Some simplified NP-complete problems

1974 ◽  
Author(s):  
M. R. Garey ◽  
D. S. Johnson ◽  
L. Stockmeyer
Keyword(s):  
Complete Problems ◽  
Np Complete
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