Finite limits and monotone computations: The lower bounds criterion

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn , Issue , 1997, Pages 302-313

  Jukna, S ^a  

^a UNIVERSITY OF TRIER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY;

FINITE LIMITS; LOWER BOUNDS; MONOTONE CIRCUIT; OR GATES; REAL-VALUED FUNCTIONS; THRESHOLD GATES; THRESHOLD-VALUE;

COMPUTER CIRCUITS;

EID: 85041119699     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.1997.612325     Document Type: Conference Paper

References (31)

1. N. Alon and R. Boppana, The monotone circuit com-plexity of Boolean functions, Combinatorica, 7: 1 (1987), pp. 1-22.
2. K. Amano and A. Maruoka, Potential of the approximation method. In: Proc. of the 37th Arm. IEEE Symp. Found. Comput. ScL, 1996.
3. A. E. Andreev, On a method for obtaining lower bounds for the complexity of individual monotone functions. Soviet Math. Dokl. 31 (3): 530-534, 1985.
4. -, On one method of obtaining effective lower bounds of monotone complexity. Algebra i logika, 26 (1): 3-21, 1987. In Russian.
5. L. Babai, A. Gal and A. Wigderson, Superpolynomial lower bounds for monotone span programs. Manuscript, 1996.
6. M. Bonet, T. Pitassi, and R. Raz, Lower bounds for cutting planes proofs with small coefficients. In: Proc. Twenty-seventh Ann. ACM Symp. Theor. Corn-put., (1995), 575-584.
7. Ch. Berg and S. Ulfberg, Symmetric approximation arguments for monotone lower bounds without sunflowers, (manuscript, 1996)
8. W. Cook, C. R. Coullard, and Gy. Turan, On the complexity of cutting plane proofs. Disc. Appl. Math., (1987), 25-38.
9. S. Cook and A. Rosenbloom, Some results on monotone real circuits, (manuscript, 1996)
10. P. Erdos and R. Rado, Intersection theorems for systems of sets. Journal of London Math. Society 35 (1969), 85-90.
11. A. Haken, The intractability of resolution, Theor. Comp. ScL, 39 (1985), 297-308.
12. -, Counting Bottlenecks to Show Monotone P/NP, In Proc. of the 36th Ann. IEEE Symp. Found. Comput. ScL, 1995.
13. A. Haken and S. Cook, An exponential lower bound for the size of monotone real circuits, Manuscript, 1995.
14. J. Hastad, S. Jukna and P. Pudlak, Top-down lower bounds for depth-three circuits, Computational Complexity, 5 (1995), 99-112.
15. S. Jukna, A criterion for monotone circuit complexity, (unpublished manuscript, 1991) [Avilable at: http://www. informat ik. uni-trier. de/~j ukna/papers/]
16. -, Finite limits and lower bounds for circuit size. Tech. Rep. Nr. 94-06, Informatik, University of Trier, 1994.
17. -, Computing threshold functions by depth-3 threshold circuits with smaller thresholds of their gates, Information Processing Letters, 56 (1995), 147-150.
18. -, Finite limits and monotone computations over the reals. ECCC Technical Report #96-026-01 (April 1996)
19. M. Karchmer, On proving lower bounds for circuit size, In Proc. of the 8th Ann. Symp. on Structure in Complexity Theory, (1993).
20. M. Karchmer and A. Wigderson, Characterizing non-deterministic circuit size. In Proc. of the 25th ACM Symposium on Theory of Computing, (1993)
21. M. Klawe, W. Paul, N. Pippenger, and M. Yannakakis, On monotone formulae with restricted depth. In Proc. of 16th ACM Symp. on Theory of Computing (1984), 480487.
22. P. Pudlak Lower bounds for resolution and cutting planes proofs and monotone computations. Submitted to Journal of Symbolic Logic, 1995.
23. A. A. Razborov, Lower bounds for the monotone complexity of some Boolean functions, Soviet Math. Dokl., 31: 354-357, 1985.
24. -, Lower bounds of monotone complexity of the logical permanent function. Mathem. Notes of the Academy of Sci. of the USSR, 37: 485-493, 1985.
25. -, Lower bounds on the monotone complexity of Boolean functions. In: Proc. of Int. Congress of Mathematicians (Berkeley, California, USA, 1986), 1987, pp. 1478-1487.
26. -, On the method of approximations. In Proc. of the 21th Ann. ACM Symp. Theor. Comput. (1989), pp. 167-176.
27. J. Simon and S. Tsai, A note on the bottlenecks counting argument. In: Proc. of 12-th Ann. IEEE Conf. on Computational Complexity, 1997 (this volume).
28. M. Sipser, A topological view of some problems in complexity theory. In Colloquia Mathematica Societatis Jdnos Bolyai 44 (1985), pp 387-391.
29. -, Personal communication, (1991)
30. E. Tardos, The gap between monotone and non-monotone circuit complexity is exponential, Combinatorica, 7: 4 (1987), pp. 141-142
31. A. C. Yao, Circuits and local computations, In Proc. 21th Ann. ACM Symp. Theor. Comput., (1989), 186196.