Multiparty communication complexity and very hard functions
نویسنده
چکیده
A boolean function f(x1, . . . , xn) with xi ∈ {0, 1}m for each i is hard if its nondeterministic multiparty communication complexity (introduced in [in: Proceedings of the 30th IEEE FOCS, 1989, p. 428–433]), C(f), is at least nm. Note that C(f) nm for each f(x1, . . . , xn) with xi ∈ {0, 1}m for each i. A boolean function is very hard if it is hard and its complementary function is also hard. In this paper, we show that randomly chosen boolean function f(x1, . . . , xn) with xi ∈ {0, 1}m for each i is very hard with very high probability (for n 3 and m large enough). In [in: Proceedings of the 12th Symposium on Theoretical Aspects of Computer Science, LNCS 900, 1995, p. 350–360], it has been shown that if f(x1, . . . , xk , . . . , xn) = f1(x1, . . . , xk) · f2(xk+1, . . . , xn), where C(f1) > 0 and C(f2) > 0, then C(f) = C(f1)+ C(f2). We prove here an analogical result: If f(x1, . . . , xk , . . . , xn) = f1(x1, . . . , xk)⊕ f2(xk+1, . . . , xn) then DC(f) = DC(f1)+ DC(f2), where DC(g) denotes the deterministic multiparty communication complexity of the function g and “⊕” denotes the parity function. © 2004 Elsevier Inc. All rights reserved.
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ورودعنوان ژورنال:
- Inf. Comput.
دوره 192 شماره
صفحات -
تاریخ انتشار 2004