Minimum propositional proof length is NP-hard to linearly approximate

Journal of Symbolic Logic

Volumn 66, Issue 1, 2001, Pages 171-191

  Alekhnovich, Michael ^d   Buss, Sam ^a   Moran, Shlomo ^b   Pitassi, Toniann ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c University of Arizona   (United States)

^d NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035590599     PISSN: 00224812     EISSN: None     Source Type: Journal    
DOI: 10.2307/2694916     Document Type: Article

References (26)

1. M. ALEHKNOVICH, S. BUSS, S. MORAN, and T. PITASSI, Minimum propositional proof length is NP-hard to linearly approximate (extended abstract), Mathematical foundations of computer science (mfcs'98), Lecture Notes in Computer Science #1450, Springer Verlag, 1998, pp. 176-184.
2. S. ARORA, L. BABAI, J. STERN, and Z. SWEEDYK, The hardness of approximate optima in lattices, codes, and systems of linear equations, Journal of Computer and System Sciences, vol. 54 (1997), pp. 317-331, Earlier version in Proceedings of the 34th Symposium on the Foundations of Computer Science, 1993, pp.724-733.
3. S. ARORA, L. BABAI, J. STERN, and Z. SWEEDYK, The hardness of approximate optima in lattices, codes, and systems of linear equations, Journal of Computer and System Sciences, vol. 54 (1997), pp. 317-331, Earlier version in Proceedings of the 34th Symposium on the Foundations of Computer Science, 1993, pp.724-733.
4. S. ARORA and C. LUND, Hardness of approximations, Approximation algorithms for NP-hard problems (D. S. Hochbaum, editor), PWS Publishing Co., Boston, 1996.
5. P. BEAME, R. IMPAGLIAZZO, J. KRAJÍČEK, T. PITASSI, and P. PUDLÁK, Lower bounds on Hilbert's Nullstellensatz and propositional proofs, Proceedings of the London Mathematical Society, vol. 73 (1996), pp. 1-26.
6. P. BEAME and T. PITASSI, Simplified and improved resolution lower bounds, 37th annual symposium on foundations of computer science, IEEE Computer Society Press, Los Alamitos, California, 1996, pp. 274-282.
7. M. BELLARE, Proof checking and approximation: Towards tight results, SIGACT News, vol. 27 (1996), pp. 2-13, Revised version at http://www-cse.ucsd.edu/users/mihir.
8. M. BELLARE, S. GOLDWASSER, C. LUND, and A. RUSSELL, Efficient probabalistically checkable proofs and applications to approximation, Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 1993, pp. 294-304.
9. M. BONET, R. GAVALDA, C. DOMINGO, A. MACIEL, and T. PITASSI, No feasible interpolation or automatization for bounded-depth frege systems, 1998, Manuscript.
10. M. L. BONET, The Lengths of Propositional Proofs and the Deduction Rule, Ph.D. thesis, U.C. Berkeley, 1991.
11. 0-Frege proofs, Proceedings of the 38th annual symposium on foundations of computer science, IEEE Computer Society, Piscataway, New Jersey, 1997, pp. 264-263.
12. S. R. BUSS, Some remarks on lengths of propositional proofs, Archive for Mathematical Logic, vol. 34 (1995), pp. 377-394.
13. S.R. BUSS, On Gödel's theorems on lengths of proofs. II. Lower bounds for recognizing k symbol provability, Feasible mathematics II (P. Clote and J. Remmel, editors), Birkhäuser Boston, Boston, MA, 1995, pp. 57-90.
14. M. CLEGG, J. EDMONDS, and R. IMPAGLIAZZO. Using the Groebner basis algorithm to find proofs of unsatisfiability. Proceedings of the twenty-eighth annual acm symposium on the theory of computing (New York). Association for Computing Machinery, 1996, pp. 174-183.
15. S. A. COOK and R. A. RECKHOW, The relative efficiency of propositional proof systems, this JOURNAL, vol. 44 (1979), pp. 36-50.
16. I. DINUR and S. SAFRA, On the hardness of approximating label cover, Technical Report TR99-015, ECCC. 1999, http://www.eccc.uni-trier.de.
17. M. H. GOLDWASSER and R. MOTWANI, Intractability of assembly sequencing: Unit disks in the plane, Proceedings of the Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science #1272, Springer-Verlag, 1997, pp. 307-320.
18. _ , Complexity measures for assembly sequences, International Journal of Computational Geometry & Applications, vol. 9 (1999), pp. 371-417.
19. K. IWAMA, Complexity of finding short resolution proofs, Mathematical foundations of computer science 1997, Lecture Notes in Computer Science #1295, Springer-Verlag, 1997, pp. 309-318.
20. K. IWAMA and E. MIYANO, Intractibility of read-once resolution, Proceedings of the Tenth Annual Conference on Structure in Complexity Theory, IEEE Computer Society, Los Alamitos, California, 1995, pp. 29-36.
21. S. KHANNA, M. SUDAN, and L. TREVISAN, Constraint satisfaction: the approximability of minimization problems, Twelfth annual ieee conference on computational complexity, IEEE Computer Society, 1997, pp. 282-296.
22. 2 and EF, Logic and computational complexity (D. Leivant, editor), Lecture Notes in Computer Science #960, Springer-Verlag, Berlin, 1995, pp. 210-220.
23. C. LUND and M. YANNAKAKIS, On the hardness of approximating minimization problems, Journal of the Association for Computing Machinery, vol. 41 (1994), pp. 960-981.
24. R. RAZ and S. SAFRA, A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP, Proceedings of the 29-th Annual ACM Symposium on Theory of Computing, 1997, pp. 475-484.
25. R. A. RECKHOW, On the Lengths of Proofs in the Propositional Calculus, Ph.D. thesis, Department of Computer Science, University of Toronto, 1976, Technical Report #87.
26. R. STATMAN, Complexity of derivations from quantifier-free Horn formulae, mechanical introduction of explicit definitions, and refinement of completeness theorems, Logic colloquium '76 (R. Gandy and M. Hyland, editors), North-Holland, Amsterdam, 1977, pp. 505-517.