Communication complexity of simultaneous messages

SIAM Journal on Computing

Volumn 33, Issue 1, 2003, Pages 137-166

  Babai, Lászlo ^a   Gál, Anna ^b   Kimmel, Peter G ^c   Lokam, Satyanarayana V ^d  

^a THE UNIVERSITY OF CHICAGO   (United States)

^b University of Texas at Austin   (United States)

^c NORTHEASTERN ILLINOIS UNIVERSITY   (United States)

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

Author keywords

Circuit complexity; Communication complexity; Group theory; Lower bounds

Indexed keywords

BOOLEAN FUNCTIONS; BOUNDARY CONDITIONS; GAME THEORY; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; POLYNOMIALS; RANDOM PROCESSES; SET THEORY; THEOREM PROVING;

CIRCUIT COMPLEXITY; COMMUNICATION COMPLEXITY; GROUP THEORY; HAMMING DISTANCE; LOWER BOUNDS; MULTIPARTY COMMUNICATION GAME; SIMULTANEOUS MESSAGES;

COMPUTATIONAL COMPLEXITY;

EID: 12144289151     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539700375944     Document Type: Article

References (35)

1. 1-formulae on finite structures, Ann. Pure Appl. Logic, 24 (1983), pp. 1-48.
2. N. Alon and J. H. Spencer, The Probabilistic Method, 2nd ed., Wiley, New York, 2000.
3. A. Ambainis, Upper bounds on multiparty communication complexity of shifts, in Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Comput. Sci. 1046, Springer, Berlin, 1996, pp. 631-642.
4. A. Ambainis and S. V. Lokam, Improved upper bounds on simultaneous messages complexity, in Proceedings of LATIN 2000, Lecture Notes in Comput. Sci. 1776, Springer, Berlin, 2000, pp. 207-216.
5. L. Babai and P. Erdös, Representation of group elements as short products, Ann. Discrete Math., 12 (1982), pp. 21-26.
6. L. Babai, T. Hayes and P. Kimmel, The cost of the missing bit: Communication complexity with help, Combinatorica, 21 (2001), pp. 455-488.
7. L. Babai, P. Kimmel, and S. V. Lokam, Simultaneous messages vs. communication, in Proceedings of the 12th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Comput. Sci. 900, Springer, Berlin, 1995, pp. 361-372.
8. L. Babai, N. Nisan, and M. Szegedy, Multiparty protocols, pseudorandom generators for logspace and time-space trade-offs, J. Comput. System Sci., 45 (1992), pp. 204-232.
9. R. Beigel and J. Tarui, On ACC, in Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, San Juan, PR, 1991, pp. 783-792.
10. Z. Bar-Yossef, T. S. Jayram, R. Kumar and D. Sivakumar, Information theory methods in communication complexity, in Proceedings of the 17th IEEE Conference on Computational Complexity, Montreal, QB, Canada, 2002, pp. 72-81.
11. B. Bollobás, Random Graphs, Academic Press, London, 1985.
12. A. K. Chandra, M. L. Furst, and R. J. Lipton, Multiparty protocols, in Proceedings of the 15th Annual ACM Symposium on Theory of Computing, Boston, MA, 1983, pp. 94-99.
13. T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley, New York, 1991.
14. P. Erdöos, R. Grahan, and E. Szemerédi, On sparse graphs with dense long paths, Comp. and Maths. with Appls., 1 (1975), pp. 365-369.
15. M. Furst, J. Saxe, and M. Sipser, Parity, circuits, and the polynomial time hierarchy, Math. Systems Theory, 17 (1984), pp. 13-27.
16. V. Grolmusz, The BNS lower bound for multi-party protocols is nearly optimal, Inform. and Comput., 112 (1994), pp. 51-54.
17. J. Håstad and M. Goldmann, On the power of small-depth threshold circuits, Comput. Complexity, 1 (1991), pp. 113-129.
18. A. Hajnal, W. Maass, P. Pudlák, M. Szegedy, and G. Turán, Threshold circuits of bounded depth, in Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science, Los Angeles, CA, 1987, pp. 99-110.
19. J. Katz and L. Trevisan, On the efficiency of local decoding procedures for error-correcting codes, in Proceedings of the 32nd ACM Symposium on Theory of Computing, Partland, OR, 2000, pp. 80-86.
20. G. Kozma and A. Lev, On H-bases and H-decompositions of finite solvable and alternating groups, J. Number Theory, 49 (1994), 385-391.
21. E. Kushilevitz and N. Nisan, Communication Complexity, Cambridge University Press, Cambridge, UK, 1997.
22. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Elsevier, Amsterdam, 1977.
23. E. Mann, Private Access to Distributed Information, Masters thesis, Technion, Haifa, Israel, 1998.
24. Y. Mansour, N. Nisan, and P. Tiwari, The computational complexity of universal hashing, Theoret. Comput. Sci., 107 (1993), pp. 121-133.
25. N. Nisan and A. Wigderson, Rounds in communication complexity revisited, SIAM J. Comput., 22 (1993), pp. 211-219.
26. P. Pudlák and V. Rödl, Modified ranks of tensors and the size of circuits, in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, San Diego, CA, 1993, pp. 523-531.
27. P. Pudlák, V. Rödl, and J. Sgall, Boolean circuits, tensor ranks, and communication complexity, SIAM J. Comput., 26 (1997), pp. 605-633.
28. L. Pyber, On the Rohrbach Conjecture, private communication.
29. Ω(log n) lower bounds on the size of depth 3 circuits with AND gates at the bottom, Inform. Process. Lett., 45 (1993), pp. 303-307.
30. H. Rohrbach, Ein Beitrag zur additiven Zahlentheorie, Math. Z., 42 (1937), pp. 1-30.
31. H. Rohrbach, Anwendung eines Satzes der additiven Zahlentheorie auf eine gruppentheoretische Frage, Math. Z., 42 (1937), pp. 538-542.
32. W. M. Schmidt, Equations over Finite Fields: An Elementary Approach, Lecture Notes in Math. 536, Springer, Berlin, 1976.
33. L. Valiant, Graph-theoretic arguments in low-level complexity, in Proceedings of 6th Symposium on Mathematical Foundations on Computer Science, Lecture Notes in Comput. Sci. 53, Springer, Berlin, 1977, pp. 162-176.
34. A. C.-C. Yao, Lower bounds of probabilistic arguments, in Proceedings of the 24th Annual IEEE Symposium on Foundations of Computer Science, Tucson, AZ, 1983, pp. 420-428.
35. A. C.-C. Yao, On ACC and threshold circuits, in Proceedings of the 31st Annual IEEE Symposium on Foundations of Computer Science, St. Louis, MO, 1990, pp. 619-627.