Lower bounds on Hilbert's Nullstellensatz and propositional proofs

Proceedings of the London Mathematical Society

Volumn 73, Issue 1, 1996, Pages 1-26

  Beame, Paul ^a   Impagliazzo, Russell ^c   Krajíček, Jan ^b   Pitassi, Toniann ^d   Pudlák, Pavel ^b  

^a University of Washington   (United States)

^b INSTITUTE OF MATHEMATICS   (Czech Republic)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d University of Pittsburgh   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002040451     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/plms/s3-73.1.1     Document Type: Article

References (20)

1. M. AJTAI, 'The complexity of the pigeonhole prindple', Proceedings of the IEEE 29th Annual Symposium on the Foundation of Computer Science (IEEE, Piscataway, N.J., 1988), pp. 346-355.
2. M. AJTAI, 'Parity and the pigeonhole principle', Feasible mathematics (eds S. R. Buss and P.J. Scott, Birkhaüser, Basel, 1990), pp. 1-24.
3. M. AJTAI, 'Symmetric systems of linear equations modulo p', Research report RJ 9422 (82 674), IBM Almaden Research Center, 1993.
4. M. AJTAI, 'The independence of the modulo p counting principles', Proceedings of the 26th Annual ACM Symposium on the Theory of Computing (ACM Press, New York, 1994), pp. 402-417.
5. P. BEAME, 'A switching lemma primer', Technical Report 95-07-01, Department of Computer Science and Engineering, University of Washington, 1993.
6. P. BEAME, R. IMPAGLIAZZO, J. KRAJÍČEK, T. PITASSI, P. PUDLÁK, and A. WOODS, 'Exponential lower bounds for the pigeonhole principle', Proceedings of the 24th Annual ACM Symposium on the Theory of Computing (ACM Press, New York, 1992), pp. 200-221.
7. P. BEAME and T. PITASSI, 'An exponential separation between the matching principles and the pigeonhole principle', Ann. Pure. Appl. Logic to appear.
8. D. BROWNAWELL, 'Bounds for the degrees in the Nullstellensatz', Ann. of Math. (2) 126 (1987) 577-591.
9. L. CANIGLIA, A. GALLIGO, and J. HEINTZ, 'Some new effectivity bounds in computational geometry', Proceedings of the 6th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (ed. T. Mora), Lecture Notes in Computer Science 357 (Springer, Berlin, 1989), pp. 131-151.
10. S. A. COOK and A. R. RECKHOW, 'The relative efficiency of propositional proof systems', J. Symbolic Logic 44 (1979) 36-50.
11. A. HAKEN, 'The intractability of resolution', Theoret. Comput. Sci. 39 (1985) 297-308.
12. J. HȦSTAD, Computation limits of small depth circuits, ACM dissertation award 1986 (MIT Press, Cambridge, Mass, 1987).
13. J. KOLLÁR, 'Sharp effective Nullstellensatz', J. Amer. Math. Soc. 1 (1988) 963-975.
14. J. KRAJÍČEK, 'Lower bounds to the size of constant-depth propositional proofs', J. Symbolic Logic 59 (1994) 73-86.
15. J. KRAJÍČEK, Bounded arithmetic, propositional logic, and complexity theory (Cambridge University Press, 1995).
16. J. KRAJÍČEK, P. PUDLÁK, and A. WOODS, 'Exponential lower bound to the size of bounded depth Frege proofs of the pigeonhole principle', Random Structures Algorithms 7 (1995) 15-39.
17. J. B. PARIS and A. J. WILKIE, 'Counting problems in bounded arithmetic', Methods in mathematical logic, Lecture Notes in Mathematics 1130 (Springer, Berlin, 1985), pp. 317-340.
18. T. PITASSI, P. BEAME, and R. IMPAGLIAZZO, 'Exponential lower bounds for the pigeonhole principle', Comput. Complexity 3 (1993) 97-308.
19. S. RIIS, 'Independence in bounded arithmetic', D.Phil, thesis, Oxford University, 1993.
20. S. RIIS, 'Count(q) does not imply Count(p)', preprint, Aarhus University, 1994.