Graph complexity and slice functions

Theory of Computing Systems

Volumn 36, Issue 1, 2003, Pages 71-88

  Lokam, Satyanarayana V ^a  

^a The Department of Civil and Environmental Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SLICE FUNCTIONS;

BOOLEAN FUNCTIONS; COMPUTATIONAL COMPLEXITY; POLYNOMIALS;

GRAPH THEORY;

EID: 0038607965     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-002-1068-0     Document Type: Article

References (34)

1. [AB] Alon, N., Boppana, R.: The Monotone Circuit Complexity of Boolean Functions, Combinatorica, 7(1) (1987), 1-22.
2. [B] Berkowitz, S.: On Some Relationships Between Monotone and Non-Monotone Circuit Complexity, Technical Report, University of Toronto, 1982.
3. [BFS] Babai, L., Frankl, P., Simon, J.: Complexity Classes in Communication Complexity Theory, Proc. 26th IEEE FOCS, 1986, pp. 337-347.
4. [D] Dunne, P.: The Complexity of Central Slice Functions, Theoret. Comput. Sci., 44 (1986), 247-257.
5. [F1] Forster, J.: A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity, Proc. 16th IEEE Conference on Computational Complexity (CCC), 2001, pp. 100-106.
6. [F2] Friedman, J.: Constructing O(n log n) Size Monotone Formulae for the kth Elementary Symmetric Polynomial of n Boolean Variables, SIAM J. Comput., 15(3) (1986), 641-654.
7. [H1] Håstad, J.: Almost Optimal Lower Bounds for Small Depth Circuits, in S. Micali (ed.), Advances in Computer Research, Vol 5: Randomness and Computation, JAI Press, Greenwich, CT, 1989.
8. [H2] Håstad, J.: The Shrinkage Exponent of de Morgan Formulas Is 2. SIAM J. Comput., 27(1) (1998), 48-64.
9. [HJP] Håstad, J., Jukna, S., Pudlák, P.: Top-Down Lower Bounds for Depth-3 Circuits, Proc. 34th IEEE FOCS, pp. 124-129.
10. [HK] Hayes, T., Kutin, S.: Personal communication.
11. [HR] Harnik, D., Raz, R.: Higher Lower Bounds on Monotone Size. Proc. ACM STOC, 2000, pp. 378-387.
12. O(n1/3), Proc. ACM STOC, 2001, pp. 258-265.
13. [KW1] Karchmer, M., Wigderson, A.: Monotone Circuits for Connectivity Require Sper-Logarithmic Depth, SIAM J. Discrete Math. 3(2) (1990), 255-265.
14. [KW2] Krause, M., Waack, S.: Variation Ranks of Communication Matrices and Lower Bounds for Depth-Two Circuits Having Symmetric Gates with Unbounded Fan-In, Proc. 32nd IEEE FOCS, 1991, pp. 777-782.
15. [L] Lokam, S. V.: Remarks on Graph Complexity, Proc. 18th FST & TCS, 1998, pp. 307-318.
16. [NS] Nisan, N., Szegedy, M.: On the Degree of Boolean Functions as Real Polynomials, Proc. 24th ACM STOC, 1991, pp. 462-467.
17. [PPZ] Paturi, R., Pudlák, P., Zane, F.: Satisfiability Coding Lemma, Proc. 38th IEEE FOCS, 1997, pp. 566-574.
18. [PR1] Pudlák, P., Rödl, V.: A Combinatorial Approach to Complexity, Combinatorica, 14 (1992), 221-226.
19. [PR2] Pudlák, P., Rödl, V.: Some Combinatorial-Algebraic Problems from Complexity Theory, Discrete Math., 136 (1994), 253-279.
20. [PRS] Pudlák, P., Rödl, V., Savický, P.: Graph Complexity, Acta Informatica, 25 (1988), 515-535.
21. [PSZ] Paturi, R., Saks, M., Zane, F.: Exponential Lower Bounds on Depth 3 Boolean Circuits, Proc. 29th ACM STOC, 1997, pp. 86-91.
22. [R1] Razborov, A. A.: A Lower Bound on the Monotone Network Complexity of the Logical Permanent, Mat. Zametki 37(6) (1985), 887-900 (in Russian), English translation in: Math. Notes 37(6) (1985), 485-493.
23. [R2] Razborov, A. A.: Lower Bounds on the Monotone Complexity of Some Boolean Functions, Dokl. Akad. Nauk SSSR 281(4) (1985), 798-801 (in Russian), English translation in: Soviet Math. Dokl. 31 (1985), 354-357.
24. [R2] Razborov, A. A.: Lower Bounds on the Monotone Complexity of Some Boolean Functions, Dokl. Akad. Nauk SSSR 281(4) (1985), 798-801 (in Russian), English translation in: Soviet Math. Dokl. 31 (1985), 354-357.
25. [R3] Razborov, A. A.: Lower Bounds on the Size of Bounded Depth Networks Over a Complete Basis with Logical Addition, Mat. Zametki 41(4) (1987), 598-607 (in Russian), English translation in: Math. Notes 41(4) (1987), 333-338.
26. [R4] Razborov, A. A.: Applications of Matrix Methods for the Theory of Lower Bounds in Computational Complexity, Combinatorica, 10 (1990), 81-93.
27. [RM] Raz, R., McKenzie, P.: Separation of the Monotone NC Hierarchy, Proc. 38th IEEE FOCS, 1997, pp. 234-243.
28. [RW] Raz, R., Wigderson, A.: Monotone Circuits for Matching Require Linear Depth, J. Assoc. Comput. Mach., 39(3) (1992), 736-744.
29. [S] Smolensky, R.: Algebraic Methods in the Theory of Lower Bounds for Boolean Circuit Complexity, Proc. 19th STOC, 1987, pp. 77-82.
30. [T] Tardos, É.: The Gap Between Monotone and Non-Monotone Circuit Complexity Is Exponential, Combinatorica, 8(1) (1988), 141-142.
31. [V1] Valiant, L.: Graph-Theoretical Methods in Low-level Complexity, Proc. 6th MFCS, LNCS vol. 53, Springer-Verlag, Berlin, 1977, pp. 162-176.
32. [V2] Valiant, L.: Negation Is Powerless for Boolean Slice Functions, SIAM J. Comput., 15 (1986), 531-535.
33. [W] Wegener, I.: The Complexity of Boolean Functions, Wiley-Teubner Series in Computer Science, Teubner, Stuttgart/Wiley, Chichester, 1987.
34. [Y] Yao, A.: Some Complexity Questions Related to Distributive Computing, Proc. 11th ACM STOC, 1979, pp. 209-213.