M. Karchmer, I. Newman, M. Saks, A. Wigderson. Non-deterministic Communication Complexity with Few Witnesses. Journal of Computer and System Sciences, vol. 49, pp. 247--275, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the power of non determinism in Turing machine computation. In communication games non determinism is proven to be stronger than determinism (see [7] 5] 2] Analogously to the study of the power of the bounded randomness, the study of the power of the bounded non determinism has nice results [4] or [3] In [4] Karchmer, Newman, Saks and Wigderson examined communication games with bounded non determinism: for a positive integer k they introduced n k (f) the length of the shortest nondeterministic protocol for computing the function f subject to the condition that each input has at most k ....

....in Turing machine computation. In communication games non determinism is proven to be stronger than determinism (see [7] 5] 2] Analogously to the study of the power of the bounded randomness, the study of the power of the bounded non determinism has nice results [4] or [3] In [4] Karchmer, Newman, Saks and Wigderson examined communication games with bounded non determinism: for a positive integer k they introduced n k (f) the length of the shortest nondeterministic protocol for computing the function f subject to the condition that each input has at most k witnesses (de ....

[Article contains additional citation context not shown here]

M. Karchmer, I. Newman, M. E. Saks, and A. Wigderson, Non-deterministic communication complexity with few witness, Journal of Computer and System Sciences, 49 (1994), pp. 247-257.

....the power of non determinism in Turing machine computation. In communication games non determinism is proven to be stronger than determinism (see [7] 5] 2] Analogously to the study of the power of the bounded randomness, the study of the power of the bounded non determinism has nice results [4] or [3] In [4] Karchmer, Newman, Saks and Wigderson examined communication games with bounded non determinism: for a positive integer k they introduced n k (f) the length of the shortest nondeterministic protocol for computing the function f subject to the condition that each input has at most k ....

....in Turing machine computation. In communication games non determinism is proven to be stronger than determinism (see [7] 5] 2] Analogously to the study of the power of the bounded randomness, the study of the power of the bounded non determinism has nice results [4] or [3] In [4] Karchmer, Newman, Saks and Wigderson examined communication games with bounded non determinism: for a positive integer k they introduced n k (f) the length of the shortest nondeterministic protocol for computing the function f subject to the condition that each input has at most k witnesses ....

[Article contains additional citation context not shown here]

M. Karchmer, I. Newman, M. E. Saks, and A. Wigderson, Non-deterministic communication complexity with few witness, Journal of Computer and System Sciences, 49 (1994), pp. 247--257.

....of nondeterministic finite automata, with the emphasis on the tradeoff between the size and the degree of nondeterminism of nfa s. Our procedure is mainly based on the following facts: i) The theory of communication complexity contains deep results about the nature of nondeterminism (see, e.g. [KNSW94, HS96]) that use the combinatorial structure of the communication matrix as the computing problem representation. ii) In [DHRS97, Hr97] the non uniform model of communication protocols for computing finite functions was extended to a uniform model for recognizing languages in such a way that several ....

....cover of all 1 s in M L of cardinality size A . The similarity to the deterministic communication complexity is that any such protocol determines an exact cover of all elements of the communication matrix by monochromatic submatrices. Some nontrivial results from communication complexity theory [KNSW94] are needed to relate cc(L) and uns(L) via the outlined connection. Theorem 1 For every regular language L Sigma a) uns(L) RankQ (M L ) b) ns k (L) RankQ (M L ) Gamma 1. c) ns k (L) 2 cc(L) k Gamma 2. Proof: Let A be an optimal unfa for L. A can be simulated by a one way ....

[Article contains additional citation context not shown here]

Karchmer, M., Saks, M., Newman, I., Wigderson, A.: Non-deterministic communication complexity with few witnesses. Journal of Computer and System Sciences 49 (1994), 247--257.

....of nondeterministic nite automata, with the emphasis on the tradeo between the size and the degree of nondeterminism of nfa s. Our procedure is mainly based on the following facts: i) The theory of communication complexity contains deep results about the nature of nondeterminism (see, e.g. [KNSW94, HS96]) that use the combinatorial structure of the communication matrix as the computing problem representation. ii) In [DHRS97, Hr97, HS00] the non uniform model of communication protocols for computing nite functions was extended to a uniform model for recognizing languages in such a way that ....

....cover of all 1 s in ML of cardinality size A . The similarity to the deterministic communication complexity is that any such protocol determines an exact cover of all elements of the communication matrix by monochromatic submatrices. Some nontrivial results from communication complexity theory [KNSW94] are needed to relate cc(L) and uns(L) via the outlined connection. Theorem 1. For every regular language L , a) uns(L) RankQ (ML ) b) ns k (L) RankQ (ML ) 1=k 1, c) ns k (L) 2 p cc(L) k 2. Proof: Let A be an optimal unfa for L. A can be simulated by a one way ....

[Article contains additional citation context not shown here]

Karchmer, M., Saks, M., Newman, I., Wigderson, A.: Nondeterministic communication complexity with few witnesses. Journal of Computer and System Sciences 49 (1994), 247-257.

....and Reischuk in [6] and [7] studied different measures of communication complexity of discrete functions. In this paper we study counting acceptance modes for nondeterministic communication protocols introduced in [7] Certain types of counting communication complexity classes were also studied in [11]. The arising complexity classes are analogues of Turing machine based complexity classes. These were extensively studied in the last years and many oracle separations are known (cf. e.g. 5] Counting acceptance modes for communication protocols have also proved to be useful for proving lower ....

M. Karchmer, I. Newman, M. Saks, A. Wigderson, Non-deterministic communication complexity with few witnesses, Journal of Computer and System Sciences 49(1994), pp. 247-257.

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M. Karchmer, I. Newman, M. Saks, A. Wigderson. Non-deterministic Communication Complexity with Few Witnesses. Journal of Computer and System Sciences, vol. 49, pp. 247--275, 1994.

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