Hardness of minimizing and learning DNF expressions

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2008, Pages 231-240

  Khot, Subhash ^a   Saket, Rishi ^b  

^a NYU

^b Georgia Tech

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEXITY ASSUMPTIONS; DNF EXPRESSIONS; DNF FORMULAS; FIXED POSITIVE INTEGERS; LEARNABILITY; MINIMUM SIZES; POLYNOMIAL TIMES; SMALL SIZES; TRUTH TABLES;

COMPUTERS; FIBER OPTIC CHEMICAL SENSORS; POLYNOMIALS; TURBULENT FLOW;

POLYNOMIAL APPROXIMATION;

EID: 57949086063     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2008.37     Document Type: Conference Paper

References (25)

1. M. Alekhnovich, M. Braverman, V. Feldman, A. Klivans, and T. Pitassi. The complexity of properly learning simple concept classes. J. Comput. Syst Sci., 74(1): 16-34, 2008.
2. 0 circuits given a truth table. In IEEE Conference on Computational Complexity, pages 237-251, 2006.
3. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and the hardness of approximation problems. J. ACM, 45(3):501-555, 1998.
4. S. Arora and S. Safra. Probabilistic checking of proofs: A. new characterization of NP. J. ACM, 45(1):70-122, 1998.
5. O. Coudert and T. Sasao. Two level logic minimization. Kluwer Academic Publishers, 2001.
6. S. Czort. The complexity of minimizing disjunctive normal form formulas. Master's Thesis, University of Aarhus. 1999.
7. U. Feige. A threshold of ln n for approximating set cover. J. ACM, 45(4): 634-652, 1998.
8. th ACM STOC, pages 363-372, 2006.
9. V. Feldman. Optimal hardness results for maximizing agreements with monomials. In IEEE Conference on Computational Complexity, pages 226-236, 2006.
10. th IEEE FOCS, pages 563-574, 2006.
11. J. Jackson. An efficient membership-query algorithm, for learning DNF with respect to the uniform distribution. J. Comput. Syst. Sci., 55(3):414-440, 1997.
12. nd IEEE FOCS, pages 600-609, 2001.
13. S. Khot and A. Ponnuswami. Better inapproximability results for maxclique, chromatic number and min-3Lindeletion. In ICALP, pages 226-237, 2006.
14. Õ(n1/3) J. Comput. Syst. Sci., 68(2): 303-318, 2004.
15. C. Lund and M. Yannakakis. On the hardness of approximating minimization problems. J. ACM, 41(5):960-981, 1994.
16. W. Masek. Some NP-complete set covering problems. Unpublished. 1979.
17. E. McCluskey. Minimization of boolean functions. Bell Sys. Tech. Jour., 35:1417-1444, 1956.
18. R. Nock, P. Jappy, and J. Sallantin. Generalized graph colorability and compressibility of boolean formulae. In Proc. ISAAC, pages 237-246, 1998.
19. L. Pitt and L. Valiant. Computational limitations of learning from examples. J. ACM, 35(4), 1988.
20. W. Quine. The problem of simplifying truth functions. American Mathematical Monthly, 59:521-531, 1952.
21. W. Quine. A way to simplify truth functions. American Mathematical Monthly, 62:627-631, 1956.
22. R. Raz. A parallel repetition theorem. SIAM J. Comput., 27(3):763-803, 1998.
23. nd ACM STOC, pages 191-199, 2000.
24. R. Schapire. The strength of weak learnability. Machine Learning, 5:197-227, 1990.
25. th ACM STOC, pages 436-445, 1984.