A. K. Chandra, M. L. Furst, R. J. Lipton. Multi-party protocols. In Proc. of the 15th ACM Symposium on Theory of Computing, (1983), pp. 94-99.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....1.2 Communication Complexity In this paper we will obtain all our lower bounds as corollaries to known lower bounds in communication complexity models. We will use both the well studied two party model of Yao [Yao79] and the somewhat less studied multiparty model of Chandra, Furst and Lipton [CFL83] Definitions of these models appear in section 2. The basic argument is the same in all cases: If a function with high communication complexity is computed by elements each having small communication complexity, then many of these elements are required in order to compute the function. ....

.... Theta(n) in [CG85] These lower bounds show in fact that Theta(n) bits are needed even to be correct with probability slightly better than 1=2. Theorem B. R [ffl] IP n ) n=2 Gamma log ffl 2 2. 4 Multiparty protocols We will also consider the multiparty model of Chandra, Furst and Lipton [CFL83] which was also studied in [BNS89, HG91, NW91] In this model a function of k n bit strings, f( x 1 : x k ) is to be evaluated by k players, where each player i knows the values of all x j except x i . The players communicate according to a fixed protocol by taking turns writing on a ....

A. Chandra, M. Furst, and R. Lipton. Multiparty protocols. In Proceedings of the 15th ACM STOC, pages 94--99, 1983.

....are for symmetric Boolean functions, where a function is symmetric if it is invariant under permutations of the variables, i.e. f(b) depends only on the number of 1 s among b i s. The first nontrivial nonlinear lower bound was obtained using Ramsey type argument by Chandra, Furst and Lipton [65] for the function # i=1 x i = n 2 under the assumption of bounded width. It is very close to linear,## nw(n) where w(n) is the inverse of the van der Waerden numbers. Better nonlinear bound,## n log log n log log log n) was found by Pudlak [207] using a di#erent Ramsey argument for ....

A. Chandra, M. Furst and R. Lipton, Multiparty protocols, Proceedings 15th ACM STOC. (1983), 94--99.

....open questions. For instance, the Karchmer Widgerson game [15] established links between monotone circuit depth and communication complexity and later allowed Raz and McKenzie [21] to show that the monotone NC hierarchy is infinite and strictly contained in monotone P . Chandra, Furst and Lipton [7] introduced an extension of Yao s model to k players. Here, each player has some portion of the input written on his forehead and available to all but himself. This is a stronger model than the original 2 player game and only few lower bounds are known for it. These results however have many ....

....an extension of Yao s model to k players. Here, each player has some portion of the input written on his forehead and available to all but himself. This is a stronger model than the original 2 player game and only few lower bounds are known for it. These results however have many applications [1, 7], particularly in the study of circuit complexity [10, 12, 13, 14] 1.2 Finite automata, finite monoids and circuit complexity The relationship between finite monoids and regular languages has been well uncovered [9, 19] and has been exploited since the 50 s to classify these languages and ....

[Article contains additional citation context not shown here]

A. K. Chandra, M. L. Furst, and R. J. Lipton. Multi-party protocols. In Proc. ACM STOC, pages 94--99, 1983.

.... a generator that maps 2 bits and # fools all space S computations, for some # = 2 #( # S) The proof that their generator is a PRG for space bounded computation is based on a connection between small space computation and a model of multiparty communication complexity introduced in [10]. Let f(x 1 , x 2 , x k ) be a boolean function as above. In the multi party communication model, there are k parties, and the i party knows every input except x i . They communicate by means of a blackboard readable by all. The communication complexity of f is the minimum number of ....

A. Chandra, M. Furst, and R. Lipton. Multiparty protocols. In 15th ACM Symposium on Theory of Computing, pages 94--99, 1983.

....program is a leveled branching program in which all the nodes on each level are labeled with the same variable. Call the sequence of variables reached at each level the query sequence of the oblivious branching program. Multiparty communication complexity, introduced by Chandra, Furst and Lipton [10] in order to study oblivious branching programs, is an extension of the usual 2 party communication complexity. Suppose that p parties, each with unlimited computational power, wish to exchange information to compute the value of f : D f0; 1g, whose input has been divided according P = fP1 ; ....

....partition p party communication complexity of f , C p (f) to be the minimum fixed partition communication complexity of f , taken over all p partitions of the inputs into equal size sets. Several lower bounds on the multiparty communication complexity of Boolean functions have been shown in [10, 4, 11, 12, 15] in the fixed partition model. The lower bound techniques for multiparty communication complexity developed following [4] are an extension of the lower bound techniques for 2 party communication complexity which rely on analyzing the properties of functions on large combinatorial rectangles. In ....

[Article contains additional citation context not shown here]

Ashok K. Chandra, Merrick L. Furst, and Richard J. Lipton. Multi-party protocols. In Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, pages 94--99, Boston, MA, April 1983.

....same distribution for the simultaneous communication model. A lower bound of Omega Gamma n=k) in the one way model would yield strong space lower bounds for data stream algorithms for frequency moments. Finally, we visit the simultaneous communication model in the number on the forehead model [CFL83]. This model has connections to circuit complexity, and one of the important results here is that of Babai et al. BGKL96] for the problem of the generalized addressing function with k players with respect to a group G (see definition in Section 5.3) For the deterministic case, they obtain ....

....the input length) Player j gets the projection of the input on the coordinates in I j . An input partition is disjoint, if I 1 ; I k are pairwise disjoint. Two common input partitions we consider are: 1) Number in the hand (NIH) Yao79] I j = fjg, and (2) Number on the forehead (NOF) [CFL83] I j = n] n fjg. 3. Interaction Rules: the set of rules that regulate the exchange of messages between the players (e.g. which player s are allowed to send messages at any given moment, to whom a player can address a message, and which player announces the output) We consider two restricted ....

A. K. Chandra, M. L. Furst, and R. J. Lipton. Multi-party protocols. In Proceedings of the 15th Annual ACM Symposium on Theory of Computing (STOC), pages 94--99, 1983.

....open questions. For instance, the Karchmer Widgerson game [14] established links between monotone circuit depth and communication complexity and later allowed Raz and McKenzie [20] to show that the monotone NC hierarchy is infinite and strictly contained in monotone P . Chandra, Furst and Lipton [7] introduced an extension of Yao s model to k players. Here, each player has some portion of the input written on his forehead and available to all but himself. This is a stronger model than the original 2 player game and only few lower bounds are known for it. These results however have many ....

....an extension of Yao s model to k players. Here, each player has some portion of the input written on his forehead and available to all but himself. This is a stronger model than the original 2 player game and only few lower bounds are known for it. These results however have many applications [1, 7], particularly in the study of circuit complexity [9, 11, 12, 13] 1.2 Finite automata, finite monoids and circuit complexity The relationship between finite monoids and regular languages has been well uncovered [8, 18] and has been exploited since the 50 s to classify these languages and ....

[Article contains additional citation context not shown here]

A. K. Chandra, M. L. Furst, and R. J. Lipton. Multi-party protocols. In Proc. 15 th ACM STOC, pages 94--99, 1983.

....whole input with the minimal total amount of communication. It is assumed that there is a coordinator that is allowed to communicate to each party, but the parties are not allowed to communicate directly with each other. The multiparty model was introduced and investigated in [DF89] Note that in [CFL83] a different multiparty model was considered. In that model each of the n parties has all the inputs except one, and all parties communicate through a shared blackboard . This model was investigated in [BNS89] where an interesting relation to time space tradeoffs and branching programs was ....

Chandra, A. K., Furst, M. L., Lipton, R. J., Multi-party protocols, Proceedings, 15th ACM STOC, 94--99, 1983. 13

.... be found in [8] The study of the communication complexity of the two party model was inspired by the VLSI circuits complexity, cf. 10] and [13] There are many other applications of the communication complexity, cf. 9] The multiparty model was introduced and investigated in [4] Note that in [3] a different multiparty model was considered. In that model each of the n parties has all the inputs except one, and all parties communicate through a shared blackboard . This model was investigated in [1] where an interesting relation to time space tradeoffs and branching programs was ....

Chandra, A. K., Furst, M. L., Lipton, R. J., Multi-party protocols, Proceedings, 15th ACM STOC, 94--99, 1983.

.... obtaining significant branching program size lower bounds, this strategy has fostered the investigation of a wide variety of branching program restrictions (see [We87] for a partial account) One such restriction of particular interest to us is the polynomial length bounded width branching program [BoDoFiPa83, ChFuLi83]. Whereas polynomial length bounded width branching programs were thought at first to be quite weak [BoDoFiPa83] Barrington proved to the contrary [Ba86] that such programs Supported by an NSERC of Canada graduate scholarship. y Supported in part by an NSERC of Canada graduate scholarship and ....

A. Chandra, M. Furst and R. Lipton, Multi-party protocols, Proc. of the 15th ACM Symp. on the Theory of Computing (1983), pp. 94-99.

.... bandwidth model, has been studied in [17] and [18] Other work in the PRAM(m) model includes [6] 8] 15] and [23] Variants of the P PRAM(m) are studied in [4] and [16] and a related model is studied in [3] One other paper that uses related ideas from Ramsey theory for compression is [11], where Chandra, Furst and Lipton introduce multi party parallel computation in the number on the forehead model. In this model, the input is p integers a 1 : a p , and processor i knows the entire input except for a i . They demonstrate an equivalence between the communication requirements ....

A. Chandra, M. Furst, and R. Lipton. Multi-party protocols. In STOC, 1983.

....the time to construct the sample space and exhaustively search it to find a good design is negligible compared to the running time of the rest of the construction. 4 General symmetric gates 4. 1 Multiparty communication protocols Let us recall the definition of d party communication protocols [4]. Suppose [r] R 1 Delta [ R 2 Delta [ Delta Delta Delta Delta [ R d is a partition of [r] into d disjoint parts. Imagine d players, P 1 ; P 2 ; P d , who have access to an input string z 2 f0; 1g r such that P i knows all bits of z except those in positions belonging to R i ....

Chandra, A., Furst, M., and Lipton, R., "Multiparty protocols, FOCS 1983, pp. 94--99.

....first player 1, then player 2 and so on. Conjecture: For some 0 protocols of length n are not long enough to compute v k 1 or only a single bit of v k 1 . Remark 2: Communication games where player i knows everything except the i th part of the information have been introduced by Chandra, Furst, and Lipton (1983) and have been also considered by Babai, Nisan, and Szegedy (1992) They proved large lower 12 bounds for difficult functions. Their methods cannot be used here, since our game becomes trivial, if the players may write in arbitrary order. Player 2 may write v 2 and then player 1 may write v k 1 . ....

Chandra, A. K., Furst, M. L., and Lipton, R. J. (1983). Multiparty protocols. In 15th Symp. on Theory of Computing, 94--99.

....BPw (f n ) Omega i n 2 log n j for f n from the theorem 2 and this is the best bound on BPw known for w 3. A series of papers was devoted to symmetric functions. As in the section 3, we try to formulate corresponding results in terms of the MAJORITY function. Chandra, Furst and Lipton [14] showed that RSw (MAJ n ) Omega Gamma n Delta W (n) where W (n) is the inverse of van der Waerden function. Ajtai, Babai, Hajnal, Komlos, Pudl ak, Rodl, Szemeredi and Tur an [1] established the bound RSw (f n ) Omega Gamma n log n= log log n) for some symmetric f n . The following bound was ....

A. Chandra, M. Furst, and R. Lipton. Multiparty protocols. In Proceedings of the 15th ACM STOC, pages 94--99, 1983.

....Institute, AV CR, Zitn a 25, 115 67 Praha 1, Czech Republic; this work was done at Institute of Computer Science, Hebrew University, Jerusalem, Israel, supported in part by Golda Meir Postdoctoral Fellowship. 1 Introduction Multiparty games were introduced by Chandra, Furst, and Lipton [6] and have found curious applications as means of proving lower bounds on the computational complexity of explicit Boolean functions. However, in spite of many results since then, no lower bounds for multiparty games with more than log n players have been proved. Attacking the barrier of log n is ....

....the result. Thus, in the simultaneous model no communication between the players is allowed, they act independently; the twist is that they share some inputs (if k 3) The model of multiparty communication turns out to be connected to many other computational models. Chandra, Furst, and Lipton [6], who introduced the model, used it to prove that majority requires superlinear length constant width branching programs. Babai, Nisan, and Szegedy [3] demonstrate that bounds for one way communication complexity can be applied to Turing machine, branching program and formulae lower bounds. Nisan ....

A. K. Chandra, M. L. Furst, and R. J. Lipton. Multi-party protocols. In Proc. of the 15th STOC, pages 94--99. ACM, 1983.

....this to a super polynomial lower bound. Shearer (unpublished) proved an exponential lower bound for the problem of checking whether the number of 1 s in the input is a multiple of three. For width three or more, the best lower bound for a symmetric function is much smaller. Chandra et al. CFL83] were the first to prove a super linear Omega0 nW (n) length lower bound on arbitrary constant width branching programs. W (n) is the inverse of the Van der Waerden function and is less than 10 for all practical values of n. They used Ramsey theoretic arguments and as we noted, their bound is ....

Ashok K. Chandra, M. L. Furst, and Richard J. Lipton. Multi-party protocols. In Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, pages 94--99, Boston, MA, April 1983. 117

....) 2) Matching upper and lower bounds of order Theta(n log (k Gamma1) n) for k log n. Key words. Multiparty communication complexity, one way protocols, pointer jumping Subject classifications. 68C25, 68Q99 2 Damm, Jukna Sgall 1. Introduction Multiparty games were introduced by Chandra et al. 1983) and have found applications as a means of proving lower bounds on the computational complexity of explicit Boolean functions. However, in spite of many results since then, no lower bounds for multiparty games with more than log n players have been proved. Attacking the barrier of log n is ....

....The referee then announces the result. Thus, in the simultaneous model no communication between the players is allowed, they act independently; the twist is that they share some inputs (if k 3) The model of multiparty communication turns out to be connected to many other computational models. Chandra et al. 1983) , who introduced the model, used it to prove that majority requires superlinear length constant width branching programs. Babai et al. 1992) demonstrate that bounds for one way communication complexity can be applied to Turing machine, branching program and formulae lower bounds. Nisan ....

A. K. Chandra, M. L. Furst, and R. J. Lipton, Multi-party protocols. In Proc. 15th Ann. ACM Symp. Theory of Computing, 1983, 94--99.

No context found.

A. Chandra, M. Furst, and R. J. Lipton. Multi-party protocols. Proceedings of the 15th Annual ACM Symposium on Theory of Computing, pages 94--99, 1983.

No context found.

A. Chandra, M. Furst, and R. J. Lipton. Multi-party protocols. Proceedings of the 15th Annual ACM Symposium on Theory of Computing, pages 94--99, 1983.

No context found.

A. K. Chandra, M. L. Furst, R. J. Lipton. Multi-party protocols. In Proc. of the 15th ACM Symposium on Theory of Computing, (1983), pp. 94-99.

No context found.

A. K. Chandra, M. L. Furst, and R. J. Lipton, Multi-party protocols. In Proc. 15th Ann. ACM Symp. Theory of Computing, 1983, 94--99.

No context found.

A. K. Chandra, M. L. Furst and Lipton R. J. Multi-party protocols. Proc. 15th STOC, 94-99, 1983.

No context found.

A. Chandra, M. Furst, and R. Lipton. Multiparty protocols. Proceedings of the 15th Annual ACM Symposium on Theory of Computing, pages 94-99, 1983.

No context found.

Chandra, A. K., Furst, M. L., and Lipton, R. J. Multi-party protocols. In Proc. 15th ACM Symp. on Theory of Computing (Boston, Massachusetts, 25--27 Apr. 1983), pp. 94--99.

No context found.

A. Chandra, M. Furst and R. Lipton. Multi-party protocols. In Proc. of 15th ACM Symposium on Theory of Computing, pp. 94-99, 1983.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC