Lower bounds for one-way probabilistic communication complexity and their application to space complexity

Theoretical Computer Science

Volumn 157, Issue 2, 1996, Pages 139-159

  Ablayev, Farid ^a  

^a KAZAN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS; COMPUTATION THEORY; HIERARCHICAL SYSTEMS; MATHEMATICAL MODELS; PROBABILITY;

BOUNDED ERROR ERROR; COMPLEXITY LOWER BOUNDS; PROBABILISTIC COMMUNICATION COMPLEXITY;

COMPUTATIONAL COMPLEXITY;

EID: 0030570116     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-3975(95)00157-3     Document Type: Article

References (29)

1. F. Ablayev, On comparing probabilistic and deterministic automata complexity of languages, in: Proc. MFCS'89, Lecture Notes in Computer Science, Vol. 379 (Springer, Berlin, 1989) 599-605.
2. F. Ablayev, Lower bounds for one-way probabilistic communication complexity, in: Proc. ICALP'93, Lecture Notes in Computer Science, Vol. 700 (Springer, Berlin, 1993) 241-252.
3. F. Ablayev, Lower bounds for probabilistic space complexity: communication-automata approach, in: Proc. LFCS'94, Lecture Notes in Computer Science, Vol. 813 (Springer, Berlin, 1994) 1-7.
4. F. Ablayev and R. Freivalds, Why sometimes probabilistic algorithms can be more effective, in: Proc. MFCS'86, Lecture Notes in Computer Science, Vol. 233 (Springer, Berlin, 1986), 1-14.
5. N. Alon, P. Frankl and V. Rodl, Geometrical realization of set systems and probabilistic communication complexity, in: Proc. 26th Ann. IEEE Symp. on Foundations of Computer Science (Springer, Berlin, 1985) 277-280.
6. B. Chor and O. Goldreich, Unibased bits from sources of weak randomness and probabilistic communication complexity, SIAM J. Comput. 17 (1988) 230-261.
7. I. Chegis and S. Jablonsky, Logic way of control of working of electric circuits, Reports Steklov Math. Inst. Moscow 5 (1958) 270-360.
8. Phan Dinh Dieu, On a necessary condition for stochastic languages. Elektron. Inform. Kybernet. 8 (1972) 575-588.
9. P. Duris, Z. Galil and G. Schnitger, Lower bounds on communication complexity, in: Proc. 16th Ann. ACM Symp. on the Theory of Computing (1984) 81-89.
10. R. Freivalds, Fast probabilistic algorithms, in: Proc. Conf. Mathematical Foundation of Computer Science, 1979, Lecture Notes in Computer Science, Vol. 74 (Springer, Berlin, 1979) 57-69. Complexity of probabilistic versus deterministic automata, in: Baltic Computer Science Selected Papers, Lecture Notes in Computer Science, Vol. 501 (Springer, Berlin, 1991), 565-613.
11. R. Freivalds, Fast probabilistic algorithms, in: Proc. Conf. Mathematical Foundation of Computer Science, 1979, Lecture Notes in Computer Science, Vol. 74 (Springer, Berlin, 1979) 57-69. Complexity of probabilistic versus deterministic automata, in: Baltic Computer Science Selected Papers, Lecture Notes in Computer Science, Vol. 501 (Springer, Berlin, 1991), 565-613.
12. R. Gallager, Information Theory and Reliable Communication (Wiley, New York, 1968).
13. J. Gill, Computational complexity of probabilistic Turing machines, SIAM J. Comput. 6 (1977) 675-695.
14. M. Goldman, J. Hastad and A. Razborov, Majority gates vs. general weighted threshold gates, in: Proc. 7th Ann. Conf. Structure in Complexity Theory (1992) 2-13.
15. B. Halstenberg and R. Reischuk, On different models of communication, in: Proc. 20th Ann. ACM Symp. on the Theory of Computing (1988) 162-172.
16. J. Hartmanis, N. Immerman and S. Mahaney, One-way log-tape reductions, in: Proc. 19th Ann. IEEE Symp. on Foundations of Computer Science (1978) 65-71.
17. J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation (Addison-Wesley, Reading, MA, 1979).
18. J. Ja'Ja', V.K. Prasana Kumar and J. Simon, Information transfer under different sets of protocols, SIAM J. Comput. 13 (1984) 840-849.
19. T.W. Lam and W. Ruzzo, Results on communication complexity classes, J. Comput. System Sci. 44 (1992) 324-342.
20. T. Lengauer, VLSI theory, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science (Elsevier, Amsterdam, 1990) 837-868.
21. L. Lovasz, Communication complexity: a survey, in: Korte, Lovasz, Promel and Schrijver, eds., Paths, Flows and VLSI Layout (Springer, Berlin, 1990) 235-266.
22. O. Lupanov, On possibilities of syntesys of circuits based on arbitrary elements, Reports Steklov Math. Inst. Moscow 51 (1958) 158-173.
23. N. Nisan and A. Wigderson, Rounds in communication complexity revisited, SIAM J. Comput. 22 (1993) 211-219.
24. C.H. Papadimitrio and M. Sipser, Communication complexity, in: Proc. 14th ACM STOC (1983) 196-200.
25. H. Paturi and J. Simon. Probabilistic communication complexity, J. Comput. System Sci. 33 (1986), 106-123.
26. M.O. Rabin, Probabilistic automata, Inform. and Control 6 (1963) 230-244.
27. N. Solovyev, Tests (Theory, Constructing, Use) (Novosibirsk, Nauka, 1978).
28. A.C. Yao, Some complexity questions related to distributive computing, in: Proc. 11th Ann. ACM Symp. on the Theory of Computing (1979) 209-213.
29. A.C. Yao, Lower bounds by probabilistic arguments, in: Proc. 24th Ann. IEEE Symp. on Foundations of Computer Science (1983) 420-428.