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The Projection Games Conjecture and the hardness of approximation of super-SAT and related problems.
- Source :
-
Journal of Computer & System Sciences . Feb2022, Vol. 123, p186-201. 16p. - Publication Year :
- 2022
-
Abstract
- The Super-SAT (SSAT) problem was introduced in [1,2] to prove the NP-hardness of approximation of two popular lattice problems - Shortest Vector Problem and Closest Vector Problem. SSAT is conjectured to be NP-hard to approximate to within a factor of n c (c is positive constant, n is the size of the SSAT instance). In this paper we prove this conjecture assuming the Projection Games Conjecture (PGC) [3]. This implies hardness of approximation of these lattice problems within polynomial factors, assuming PGC. We also reduce SSAT to the Nearest Codeword Problem and Learning Halfspace Problem [4]. This proves that both these problems are NP-hard to approximate within a factor of N c ′ / log log n (c ′ is positive constant, N is the size of the instances of the respective problems). Assuming PGC these problems are proved to be NP-hard to approximate within polynomial factors. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LOGICAL prediction
*NP-hard problems
*HARDNESS
*GAMES
Subjects
Details
- Language :
- English
- ISSN :
- 00220000
- Volume :
- 123
- Database :
- Academic Search Index
- Journal :
- Journal of Computer & System Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 152816058
- Full Text :
- https://doi.org/10.1016/j.jcss.2021.09.002