Cutting planes, connectivity, and threshold logic

Archive for Mathematical Logic

Volumn 35, Issue 1, 1996, Pages 33-62

  Buss, Samuel R ^a   Clote, Peter ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b BOSTON COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030304213     PISSN: 09335846     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01845704     Document Type: Article

References (21)

1. Ajtai, M.: Parity and the pigeonhole principle. In: Buss, S.R., Scott, P.J: (eds.) Feasible Mathematics, pp. 1-24. Basel: Birkhäuser 1990
2. Ajtai, M., Fagin, R.: Reachability is harder for directed than for undirected finite graphs. J. Symb. Logic 55: 113-150 (1990)
3. Beame, P., Impagliazzo, R., Krajíček, J., Pitassi, T., Pudlák, P., Woods, A.: Exponential lower bounds for the pigeonhole principle. In: Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pp. 200-220. New York: Association for Computing Machinery 1992
4. Beame, P., Cook., S., Papadimitriou, C., Pitassi, T.: The relative complexity of NP search problems. Proceeding of the 27th ACM Symposium on Theory of Computing, pp. 303-314. New York: Association for Computing Machinery 1995
5. Buss, S.: The prepositional pigeonhole principle has polynomial size Frege proofs. J. Symb. Logic 52: 916-927 (1987)
6. Buss, S., Clote, P.: Threshold logic proof systems. Manuscript (May 1995)
7. Buss, S., Turán, G.: Resolution proofs of generalized pigeonhole principles. Theor. Comput. Sci. 62: 311-317 (1988)
8. Clote, P., Krajíček, J. (eds.): Arithmetic, Proof Theory and Computational Complexity, 428 p. Oxford: Oxford University Press 1993
9. Clote, P.: Cutting planes and constant depth Frege proofs. In: Proceedings of 7th Annual IEEE Symposium on Logic in Computer Science, pp. 296-307. Piscataway, NJ: IEEE Computer Science Press 1992
10. Clote, P.: Cutting plane and Frege proofs. Inf. Comput. 121: 103-122 (1995)
11. Cook, S.A., Reckhow, R.: On the relative efficiency of propositional proof systems. J. Symb. Logic 44: 36-50 (1977)
12. Cook, W., Coullard, C.R., Turan, G.: On the complexity of cutting plane proofs. Discr. Appl. Math. 18: 25-38 (1987)
13. Goerdt, A.: Cutting plane versus Frege proof systems. In: Börger, E. (ed.) Computer Science Logic 1990, vol. 552, pp. 174-194. Lecture Notes in Computer Science. Berlin Heidelberg New York: Springer 1992
14. Haken, A.: The intractability of resolution. Theor. Comput. Sci. 39: 297-305 (1985)
15. Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers, 5th edn. Oxford: Clarendon Press 1979
16. Impagliazzo, R., Pitassi, T., Urquhart, A.: Upper and lower bounds for tree-like cutting planes proofs. In: Proceedings of 9th Annual IEEE Symposium on Logic in Computer Science, pp. 220-228. Piscataway, NJ: IEEE Computer Science Press 1994
17. Krajíček, J.: On Frege and extended Frege systems. In: Clote, P., Remmel, J. (eds.) Feasible Mathematics, vol. II, pp. 284-319. Basel: Birkhäuser 1994
18. Papadimitriou, C.H.: On the complexity of the parity argument and other inefficient proofs of existence. J. Comput. System Sci. 48: 498-532 (1994)
19. Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization. London: Prentice-Hall 1982
20. Paris, J.B., Wilkie, A.J.: Counting problems in bounded arithmetic. In: di Prisco, C.A. (ed.) Methods in Mathematical Logic, pp. 317-340. Lecture Notes in Mathematics 1130. Berlin Heidelberg New York: Springer 1983
21. Urquhart, A.: Hard examples for resolution. J. Assoc. Comput. Machinery 34: 209-219 (1987)