Abstract
We study the following question: if A and B are disjoint NP-complete sets, then is A ∪ B NP-complete? We provide necessary and sufficient conditions under which the union of disjoint NP-complete sets remain complete.
- M. Agrawal. 2002. Pseudo-random generators and structure of complete degrees. In Proceedings of the 17th Annual IEEE Conference on Computational Complexity. IEEE Computer Society, 139--145. Google Scholar
Digital Library
- L. Berman and H. Hartmanis. 1977. On isomorphisms and density of NP and other complete sets. SIAM J. Comput. 6, 2, 305--322.Google Scholar
Digital Library
- S. Even, A. Selman, and Y. Yacobi. 1984. The complexity of promise problems with applications to public-key cryptography. Inform. Control 61, 2, 159--173. Google Scholar
Digital Library
- L. Fortnow, J. H. Lutz, and E. Mayordomo. 2010. Inseparability and strong hypotheses for disjoint NP pairs. In Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science (Leibniz International Proceedings in Informatics). Vol. 5. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 395--404.Google Scholar
- C. Glaßer, A. Selman, and S. Sengupta. 2005. Reductions between disjoint NP-Pairs. Inform. Comput. 200, 2, 247--267. Google Scholar
Digital Library
- C. Glaßer, A. Pavan, A. Selman, and S. Sengupta. 2006. Properties of NP-complete sets. SIAM J. Comput. 36, 2, 516--542. Google Scholar
Digital Library
- C. Glaßer, A. Selman, and L. Zhang. 2007. Canonical disjoint NP-pairs of propositional proof systems. Theor. Comput. Sci. 370, 1, 60--73. Google Scholar
Digital Library
- C. Glaßer, A. Pavan, A. Selman, and L. Zhang. 2008a. Splitting NP-complete sets. SIAM J. Comput. 37, 5, 1517--1535. Google Scholar
Digital Library
- C. Glaßer, A. Selman, S. Travers, and K. W. Wagner. 2008b. The complexity of unions of disjoint sets. J. Comput. Syst. Sci. 74, 7, 1173--1187. Google Scholar
Digital Library
- O. Goldreich. 2006. On promise problems: A survey. In Theoretical Computer Science - Essays in Memory of Shimon Even. Lecture Notes in Computer Science, vol. 3895, Springer, 254--290. Google Scholar
Digital Library
- J. Grollmann and A. Selman. 1988. Complexity measures for public-key cryptosystems. SIAM J. Comput. 17, 2, 309--355. Google Scholar
Digital Library
- R. Impagliazzo and A. Wigderson. 2001. Randomness vs. time: Derandomization under a uniform assumption. J. Comput. System Sci. 63, 4, 672--688. Google Scholar
Digital Library
- J. Jackson and R. Servedio. 2005. On learning random DNF formulas under the uniform distribution. In Proceedings of the 9th International Workshop on Randomness and Computation. Lecture Notes in Computer Science, vol. 3624, Springer, 342--353. Google Scholar
Digital Library
- V. Kabanets. 2001. Easiness assumptions and hardness tests: Trading time for zero error. J. Comput. Syst. Sci. 63, 2, 236--252. Google Scholar
Digital Library
- P. Pudlak. 2001. On reducibility and symmetry of disjoint NP-pairs. Tech. rep. TR01-044, Electronic Colloquium on Computational Complexity.Google Scholar
- A. Razborov. 1994. On provably disjoint NP pairs. Tech. rep. TR94-006, Electronic Colloquium on Computational Complexity.Google Scholar
- R. Santhanam. 2009. Circuit lower bounds for Merlin-Arthur classes. SIAM J. Comput. 39, 3, 1038--1061. Google Scholar
Digital Library
- A. Selman. 1988. Natural self-reducible sets. SIAM J. Comput. 17, 5, 989--996. Google Scholar
Digital Library
Index Terms
Unions of Disjoint NP-Complete Sets
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