I. Newman, "Private vs. common random bits in communication complexity", Information Processing Letters, 39, pp. 67--71, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....model) where the two players share a string of random bits, any sampling problem is trivial and can be solved with no communication at all. Note that for communication complexity problems it is well known that the private coins model and the public coins model have roughly the same power [New]. The model used in most discussions (of both upper and lower bounds) is the public coins model. 1.2 Our Results Our results are obtained by analyzing the communication complexity of a finite precision variation of the problem P 1 (#) defined below. For completeness, we also define a related ....

....however, that the private coins model is only slightly weaker. More precisely, any problem that can be solved with communication complexity k by a public coins protocol can also be solved with communication complexity k O(logm) by a private coins protocol (where m is the length of the inputs) [New]. Hence, the two models have roughly the same power. The results proved in this paper will be correct for both models. 2.2 Quantum Communication Complexity In the quantum communication complexity model, the two players exchange between them quantum bits (qubits) rather than classical bits. For ....

I. Newman, "Private vs. common random bits in communication complexity", Information Processing Letters, 39, pp.67--71, 1991.

....the same power as the above 1 In fact this defines the complement of the set disjointness problem. Since for the models we study the communication complexity of DISJ and its complement are equal our results hold for both. bounded error model whenever the communication complexity is above log N [Ne91]. For a communication problem P , and 0, let C (P ) denote the minimum m such that there is a (probabilistic) protocol that requires at most m bits of communication and determines the correct answer with probability at least 1 Gamma . Then C0(P ) can be taken as the deterministic ....

I. Newman, "Private vs. common random bits in communication complexity", Information Processing Letters, 39, pp. 67--71, 1991.

....between PSPACE and NEXP. 3. Isolate intriguing open questions about other exponential complexity classes and obtain partial answers to these questions. One interesting aspect of items 2 and 3 is that they use both results and proof techniques from recent papers on the complexity of solving games [KMvS94, Ne91]. Imperfect information games have been considered in several previous works in complexity theory, including [C89, CL86, KLRSS94, PR79, Re84] A crucial difference between these works and ours is that the opposing players in [C89, CL86, KLRSS94, PR79, Re84] use deterministic (pure) strategies, ....

....the value of G. Similarly, the yes instances of Value (pi; ir) are games in which player P 1 has perfect information, player P 2 has imperfect recall, and the value is at most . In Section 4 below, we use the following recent results about complexity theoretic aspects of games. Theorem 2. 1 (cf. [Ne91]) In any game with payoffs in [0; 1] each player has a nearoptimal mixed strategy that chooses uniformly at random from a logarithmic size multiset of pure strategies. Specifically, if the opponent has N pure strategies, there exists a multiset of size d(ln N) ffl 2 e such that the ....

I. Newman, "Private vs. Common Random Bits in Communication Complexity, " Information Processing Letters, 39 (1991), pp. 67--71.

.... ) To summarize we have Lemma 2: The protocol described above computes in the public coins model the identity function on instances while maintaining that the number of bits communicated is O( and the probability of error on any instance is at most 2 Gamma Omega Gamma p ) Newman [14] has considered the public coins model vs. the private coins model. He showed that CR (f) O(C pub (f) log n) which in particular implies CR (f ( O(C pub (f ( log n) Clearly, CR (f ( C pub (f ( O( Delta log Delta C pub (f) All together we have the ....

Newman, I., "Private vs. Common Random Bits in Communication Complexity", Information Processing Letters 39, 1991, pp. 67-71.

....f0; 1g, that on input n uses t samples, and tosses only n 2 log 1 ffi coins. b) A (2ffl; 2ffi) sampler, S 00 , for functions f : f0; 1g n [0; 1] that on input n uses t samples, and tosses only n 2 log 1 ffi log log 1 2ffl coins. Proof. The proof adapts a technique of Newman [N] to this context. a) Let r be the number of coin tosses used by sampler S on input n. Consider the 2 2 n Theta 2 r table where a row corresponds to a function f : f0; 1g n f0; 1g, and a column corresponds to a coin toss sequence of the sampler S. A table entry (f; ae) is bad if the ....

I. Newman, "Private vs. Common Random Bits in Communication Complexity", Information Processing Letters 39, 1991, pp. 67-71.

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I. Newman, "Private vs. common random bits in communication complexity", Information Processing Letters, 39, pp. 67--71, 1991.

No context found.

I. Newman, "Private vs. common random bits in communication complexity", Information Processing Letters, 39, pp. 67--71, 1991.

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