On graph complexity

Combinatorics Probability and Computing

Volumn 15, Issue 6, 2006, Pages 855-876

  Jukna, S ^a  

^a VILNIUS UNIVERSITY   (Lithuania)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; COMBINATORIAL CIRCUITS; COMPUTATIONAL COMPLEXITY; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

CIRCUIT COMPLEXITY; COMBINATORIAL PROBLEMS;

GRAPH THEORY;

EID: 33750315890     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548306007620     Document Type: Article

References (44)

1. 1-formulae on finite structures. Ann. Pure Appl. Logic 24 1-48.
2. Alon, N. (1986) Covering graphs by the minimum number of equivalence relations. Combinatorica 6 201-206.
3. Alon, N. (1986) Eigenvalues, geometric expanders, sorting in rounds, and Ramsey Theory. Combinatorica 6 207-219.
4. Alon, N. (1994) Explicit Ramsey graphs and orthonormal labelings. Electron. J. Combin. 1 R12, 8pp.
5. Andreev, A. E. (1986) On a family of boolean matrices. Moscow Univ. Math. Bull. 41 79-82;
6. translation from Vestnik Mask. Univ. 41 (1986) 97-100
7. Babai, L., Frankl, P. and Simon, J. (1986) Complexity classes in communication complexity. In Proc. 26th Ann. IEEE Symp. on Foundations of Comput. Sci., pp. 337-347.
8. Beigel, R. and J. Tarui (1994) On ACC. Comput. Complexity 4 350-366.
9. Bublitz, S. (1986) Decomposition of graphs and monotone size of homogeneous functions. Acta Informatica 23 689-696.
10. Chung, F. R. K., Erdos, P. and Spencer, J.(1983) On the decomposition of graphs into complete bipartite subgraphs. In Studies in Pure Mathematics, Mem. of P. Turán, pp. 95-101.
11. Duchet, P. (1979) Représentations, noyaux en théorie des graphes et hypergraphes. Thèse de Doctorat d'Etat, Université Paris VI.
12. Erdos, P. and Rényi, A. (1962) On a problem in the theory of graphs. Publ. Math. Inst. Hungar. Acad. Sci. 7 215-235.
13. Erdos, P., Goodman, A. W. and Posa, L. (1966) The representation of a graph by set intersections. Canad. J. Math. 18 106-112.
14. Frankl, P. (1982) Covering graphs by equivalence relations. Ann. Discrete Math. 12 125-127.
15. Furst, M., Saxe, J. and Sipser, M. (1984) Parity, circuits and the polynomial time hierarchy. Math. Systems Theory 17 13-27.
16. Grigoriev, D. and Razborov, A. (2000) Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields. Appl. Algebra Engrg. Comm. Comput. 10 465-487.
17. Grolmusz, V. (1998) A lower bound for depth-3 circuits with MOD m gates. Inform. Process. Lett. 67 87-90.
18. Hajnal, A., Maass, W., Pudlák, P., Szegedy, M. and Turán, G. (1993) Threshold circuits of bounded depth. J. Comput. System Sci. 46 129-154.
19. Hall, M. (1967) Combinatorial Theory, Wiley, New York and London.
20. Håstad, J. (1989) Almost optimal lower bounds for small depth circuits. In Advances in Computing Research (S. Micali, ed.), Vol. 5, pp. 143-170.
21. Håstad, J. (1998) The shrinkage exponent of de Morgan formulas is 2. SIAM J. Comput. 27 48-64.
22. Håstad, J., Jukna, S. and Pudlák, P. (1995) Top-down lower bounds for depth 3 circuits. Comput. Complexity 5 99-112.
23. Karchmer, M. and Wigderson, A. (1988) Monotone circuits for connectivity require super-logarithmic depth. In Proc. 20th Ann. ACM Symp. on the Theory of Computing, pp. 539-550.
24. Karchmer, M. and Wigderson, A. (1993) On span programs. In Proc. 8th Ann. Structures in Complexity Conference, pp. 102-111.
25. Khrapchenko, V. M. (1971) A method of determining lower bounds for the complexity of ∏-schemes. Math. Notes of the Academy of Sciences of the USSR 10 474-479.
26. Kneser, M. (1955) Aufgabe 300. Jahresber. Deutsch. Math.-Verein 58.
27. Kollár, J., Rónyai, L. and Szabó, T. (1996) Norm-graphs and bipartite Turán numbers. Combinatorica 16 399-406.
28. Kovári, P., Sós, V. T. and Turán, P. (1954) On a problem of Zarankiewicz. Colloq. Math. 3 50-57.
29. Lokam, S. V. (2003) Graph complexity and slice functions. Theory Comput Syst. 36 71-88.
30. Lovász, L. (1977) Flats in matroids and geometric graphs. In Combinatorial Surveys (P. J. Cameron, ed.), Proc. 6th British Combin. Conf., Academic Press, London, pp. 45-86.
31. Lovász, L. (1978) Kneser's conjecture, chromatic numbers and homotopy. J. Combin. Theory Ser. A 25 319-324.
32. Paturi, R., Pudlák, P. and Zane, F. (1997) Satisfiability coding lemma. In Proc. 39th Ann. IEEE Symp. on Foundations of Comput. Sci., pp. 566-574.
33. Paturi, R., Saks, M. and Zane, F. (2001) Exponential lower bounds for depth three boolean circuits. Comput. Complexity 9 1-15.
34. Pudlák, P. and Rödl, V. (1992) A combinatorial approach to complexity. Combinatorica 12 221-226.
35. Pudlák, P. and Rödl, V. (1994) Some combinatorial-algebraic problems from complexity theory. Discrete Math. 136 253-279.
36. Pudlák, P. and Rödl, V. (2004) Pseudorandom sets and explicit constructions of Ramsey graphs. In Quaderni di Matematica (J. Krajicek, ed.), Vol. 13, pp. 327-346.
37. Pudlák, P., Rödl, V. and Savicky, P. (1988) Graph complexity. Acta Informatica 25 515-535.
38. Razborov, A. A. (1987) Lower bounds for the size of circuits of bounded depth with basis {∧,⊕}. Math. Notes of the Academy of Sciences of the USSR 41 333-338.
39. Razborov, A. A. (1988) Bounded-depth formulae over the basis {&, ⊕}and some combinatorial problems. In Problems of Cybernetics, Complexity Theory and Applied Mathematical Logic (S. L Adian, ed.), VINITI, Moscow, pp. 149-166 (in Russian).
40. Razborov, A. A. (1990) Applications of matrix methods to the theory of lower bounds in computational complexity. Combinatorica 10 81-93.
41. Smolensky, R. (1987) Algebraic methods in the theory of lower bounds for Boolean circuit complexity. In Proc. 19th Ann. ACM Symp. on the Theory of Computing, pp. 77-82.
42. Valiant, L. (1977) Graph-theoretic methods in low-level complexity. In Proc. 6th Conf. on Mathematical Foundations of Computer Science, Vol. 53 of Lecture Notes in Computer Science, Springer, pp. 162-176.
43. Yao, A. C. (1985) Separating the polynomial time hierarchy by oracles. In Proc. 26th Ann. IEEE Symp. on Foundations of Comput. Sci., pp. 1-10.
44. Yao, A. C. (1990) On ACC and threshold circuits. In Proc. 31th Ann. IEEE Symp. on Foundations of Comput. Sci., pp. 619-627.