L. Babai, N. Nisan, M. Szegedy. Multiparty protocols, pseudorandom generators for Logspace, and time-space trade-offs. Journal of Comput. Syst. Sci., vol. 45 (1992), pp. 204-232.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... shown that the correlation between parity and a MOD 3 AND circuit can be written as an exponential sum (also variously known as a character sum or a generalized Gaussian sum) Evaluations of such sums were also instrumental in the communication complexity lower bound of Babai, Nisan and Szegedy [BNS] on which the H astad Goldmann [HG] result is based. Character sums, which originated with Gauss in the study of cyclotomic elds and quadratic reciprocity, have been intensively studied in the number theoretic literature (see, e.g. LN] and [Sch] Here we develop a new technique for evaluating ....

....study of cyclotomic elds and quadratic reciprocity, have been intensively studied in the number theoretic literature (see, e.g. LN] and [Sch] Here we develop a new technique for evaluating the type of sums that arise in computing correlations. The Cauchy Schwarz method used to great e ect in [BNS] while very powerful, appears not to be suciently re ned for our purposes. Instead we observe some very speci c symmetry properties of the sum that can be exploited, via the triangle inequality and various identities involving the additive and multiplicative characters over Z 3 , to obtain ....

L. Babai, N. Nisan and M. Szegedy Multiparty protocols, pseudorandom generators for logspace, and time-space trade-os, in Journal of Computer and System Sciences, 45:2 (1992), pp. 204-232.

....oblivious programs of linear length. At the same time, a simple co nondeterministic oblivious program (with AND nodes) of linear length is given, showing that as for read once programs (Section 2.2.2) the two types of nondeterminism give different computational power. Babai, Nisan, and Szegedy [BNS92] in the same spirit improve this length width tradeoff, using their lower bound for multiparty communication complexity to raise the lower bound on the length of polynomial size oblivious programs (for a different function) by a factor of lg n. Note first that the lower bound method for OBDD s is ....

L. Babai, N. Nisan, and M. Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space tradeoffs. Journal of Computer and System Sciences, 45 (1992), pp. 204--232.

....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 ....

....the k party communication complexity of the EXACTLY N function, defined as N (x 1 ; x 2 ; x k ) 1 iff x i = N where N is some n bit integer known to all. They used that result to prove a superlinear lower bound on the length of bounded width branching programs computing N . In [1], Babai, Nisan and Szegedy showed an Omega Gamma n=4 ) lower bound on the k party communication complexity of the generalized inner product GIP k , defined over an n Theta k matrix A by GIP k (A) 1 iff the number of all 1 rows of A is congruent to 0 (mod 2) They also proved a similar ....

[Article contains additional citation context not shown here]

L. Babai, N. Nisan, and M. Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. J. Comput. Syst. Sci., 45(2):204-- 232, Oct. 1992.

....programs which test the same variable at each time step along any path. For oblivious branching programs, linear length and read k for some constant k are essentially the same and several size length tradeo# lower bounds for oblivious branching programs have been shown using this connection [AM88, BNS92] Oblivious read once branching programs, known as OBDD s, have been very useful as representations of functions used in verification [Bry86, BCL 94] and so have generated significant independent interest. Borodin, Razborov, and Smolensky [BRS93] observed that read k branching programs come ....

Laszlo Babai, Noam Nisan, and Mario Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-o#s. Journal of Computer and System Sciences, 45(2):204--232, October 1992.

....best lower bounds in the oblivious case have all been obtained using some form of communication complexity. Using two party communication complexity, Alon and Maass [AM88] derived lower bounds of the form T = n log(n=S) and using multi party communication complexity, Babai, Nisan, and Szegedy [BNS92] derived the best current lower bounds which are of the form T = n log (n=S) The use of rectangles in our results as well as all those referenced in Table 1 is related to 2 party communication complexity (see e.g. KN97] and most of the difficulty in these arguments is in extending the ....

....provides an alternate way to obtain the same bounds as [AM88] for oblivious branching programs (see the discussion prior to Lemma 4. 3) Recently, these methods have been extended [BV02] to include multi party communication complexity ideas which yield an alternate way to obtain the bounds of [BNS92] for oblivious branching programs. These results also extend the technique of [BJS01] using multi party communication complexity ideas to obtain lower bounds over large domains. However, it is not at all clear if it is possible to extend results to include multi party communication complexity ....

Laszlo Babai, Noam Nisan, and Mario Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. Journal of Computer and System Sciences, 45(2):204--232, October 1992.

.... our argument we give an alternative, conceptually simple proof, based on the ideas in the recent lower bounds for general branching programs, of the relationship between multiparty communication complexity and time space tradeoffs for oblivious branching programs shown by Babai, Nisan, and Szegedy [4]. Using this we obtain time space tradeoff lower bounds of the form T = n=S) for 1GAP on oblivious branching programs. Since 1GAP , the canonical complete problem for L, has a trivial general branching program of time n and width n (and therefore space O(log n) this provides the first ....

....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]

Laszlo Babai, Noam Nisan, and Mario Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. Journal of Computer and System Sciences, 45(2):204--232, October 1992.

....multiparty games where k players try to compute a k argument function. Each player has part of the input written on his forehead so that this information is available to all but himself. This model is stronger than the original 2 party model, hence lower bounds for it are difficult to prove. [2, 6] However these results also have many applications in the study of bounded width branching programs [6] pseudorandomness [2] and circuit complexity [8, 9, 10, 15] A lot of research in complexity theory has been devoted to the study of algebraic properties of languages in certain complexity ....

....so that this information is available to all but himself. This model is stronger than the original 2 party model, hence lower bounds for it are difficult to prove. 2, 6] However these results also have many applications in the study of bounded width branching programs [6] pseudorandomness [2], and circuit complexity [8, 9, 10, 15] A lot of research in complexity theory has been devoted to the study of algebraic properties of languages in certain complexity classes. This algebraic 1 approach has been particularly successful in automata theory, where the connections between regular ....

[Article contains additional citation context not shown here]

L. Babai, N. Nisan, and M. Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. J. Comput. Syst. Sci., 45(2):204--232, Oct. 1992.

....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 ....

....complexity of the EXACTLY k N function, defined as EXACTLY k N (x 1 ; x 2 ; x k ) 1 iff X x i = N where N is some n bit integer known to all. They used that result to prove a superlinear lower bound on the length of bounded width branching programs computing EXACTLY k N . In [1], Babai, Nisan and Szegedy showed an Omega Gamma n=4 k ) lower bound on the k party communication complexity of the generalized inner product GIP k , defined over an n Theta k matrix A by GIP k (A) 1 iff the number of all 1 rows of A is congruent to 0 (mod 2) They also proved a similar ....

[Article contains additional citation context not shown here]

L. Babai, N. Nisan, and M. Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. J. Comput. Syst. Sci., 45(2):204-- 232, Oct. 1992.

....logspace, and hence to derandomize BPL, the class of languages accepted by logspace randomized Turing machines with bounded two sided error. Theorem 5.17 If there is a Boolean function f 2 DSPACE[n] that requires branching programs of size 2 n) then BPL = L. Along the lines of Babai et al. BNS92] the pseudo random generators behind Theorem 5.17 let us conclude: Corollary 5.18 If there is a Boolean function f 2 DSPACE[n] that requires branching programs of size 2 n) then we can construct universal traversal sequences in logspace. The proof of Theorem 5.17 goes along the lines of the ....

L. Babai, N. Nisan, and M. Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-os. Journal of Computer and System Sciences, 45:204-232, 1992.

....which test the same variable at each time step along any path. For oblivious branching programs, linear length and read k for some constant k are essentially the same and several size length tradeoff lower bounds for oblivious branching programs have been shown using this connection [AM88, BNS92] Oblivious read once branching programs, known as OBDD s, have been very useful as representations of functions used in verification [Bry86, BCL 94] and so have generated significant independent interest. Borodin, Razborov, and Smolensky [BRS93] observed that read k branching programs come ....

L'aszl'o Babai, Noam Nisan, and M'ari'o Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. Journal of Computer and System Sciences, 45(2):204--232, October 1992.

....been 1 Since the publication of a preliminary version of our results, Ajtai [Ajt99a] see also [Ajt99b] using related techniques, has exhibited an explicit family of boolean functions for which any linear size branching program must have exponential size. 3 shown using this connection [AM88, BNS92] Oblivious read once branching programs, known as OBDD s, have been very useful as representations of functions used in verification [Bry86, BCL 94] and so have generated significant independent interest. Borodin, Razborov, and Smolensky [BRS93] observed that read k branching programs come ....

Laszlo Babai, Noam Nisan, and Mario Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-o#s. Journal of Computer and System Sciences, 45(2):204--232, October 1992.

....# 0,1, m 1 such that f(x) 0 if and only if P (x) # S. The smallest degree of polynomials P weakly representing f is called the weak mod m degree of f . We give here an###33 n) lower bound for the weak degree of the generalized inner product function (GIP) of Babai, Nisan, and Szegedy [BNS92]. This is the first lower bound result for the weak degree of a Boolean function that does not deteriorate if the number of prime divisors of m increases. In the second part of the paper, we give superpolynomial lower Abstract 2 bounds for the number of monomials with nonzero coe#cients in ....

....only two distinct prime divisors. More generally, if the number of distinct prime divisors of m is r, and the smallest prime divisor is q, then their lower bound is #(OR,m)# # 1 (q 1) o(1) # (log n) 1 (r 1) 1) The following function was first defined by Babai, Nisan, and Szegedy 1 5 [BNS92]: Definition 2 Let A # 0,1 lk .LetGIP l,k (A) denote the number of all 1 rows in matrix A, mod 2. This is the mod 2 generalized inner product of the columns of A. Here we show an##216 n) lower bound for #(GIP l,k ,m) where m is an 1 6 arbitrary integer (i.e. our lower bound does not ....

[Article contains additional citation context not shown here]

Laszlo Babai, Noam Nisan, and Mario Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space tradeo #s. Journal of Computer and System Sciences, 45:204--232, 1992.

....d threshold gate) if f can be expressed as a sign of a real polynomial of degree at most d. Then he has built a random (d 1) party protocol using the results of [19] which evaluates the d threshold gates with a small number of communicated bits, and then, using the BNS lower bound [2], the size lower bound of Omega Gamma c d n= log 2 n) follows for d = O(log n) We instead of symmetricity or degree conditions require the L 1 norms of the gate functions to be small, so Boolean gates with non zero large degree coefficients are also allowed. We say that a Boolean ....

....of depth 2 circuits with a MAJORITY gate at the top, and linear threshold gates of small weights on the bottom. Hastad and Goldmann [19] generalized it to circuits with a MAJORITY gate at the top and d threshold gates with small weights at the bottom, d = O(log n) using the BNS lower bound [2]. 7 Nisan [26] generalizing the results of [17] and [19] also gives an exponential lower bound to the size of those depth 2 circuits, which compute GIP, with a MAJORITY gate at the top, and several d threshold gates of arbitrary weights at the bottom, for d = O(log n) We prove here an ....

L. Babai, N. Nisan, and M. Szegedy, Multiparty protocols, pseudorandom generators for logspace, and time--space trade-offs, Journal of Computer and System Sciences, 45 (1992), pp. 204--232.

....BPL, the class of languages accepted by logspace randomized Turing machines with bounded two sided error. Theorem 5.17 If there is a Boolean function f 2 DSPACE[n] such that C f (n) 2 2 Omega Gamma n) then BPL = L. 12 We refer to Appendix C for a proof. Along the lines of Babai et al. BNS92] the pseudo random generators behind Theorem 5.17 let us conclude: Corollary 5.18 If there is a Boolean function f 2 DSPACE[n] such that C f (n) 2 2 Omega Gamma n) then we can construct universal traversal sequences in logspace. 6 Conclusions In this paper, we have demonstrated the power ....

L. Babai, N. Nisan, and M. Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. Journal of Computer and System Sciences, 45:204--232, 1992.

....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 and Wigderson [13] have shown, using a result of Valiant [17] that a lower bound (n= log log n) on 3 party simultaneous protocols for a function f ....

....in circuit complexity. The best lower bound for the general, one way, or even simultaneous multiparty complexity is an Omega Gamma n=2 k ) lower bound of Chung and Tetali [7] for generalized inner product, improving an earlier bound Omega Gamma n=c k ) of Babai, Nisan, and Szegedy [3]. This means that we have no lower bounds at all for k log n. Pointer jumping is often considered in the context of lower bounds and communication complexity (e.g. 14, 9, 10, 13, 5, 16] This is an important function, since it simulates many naturally occurring functions, e.g. shifting, ....

[Article contains additional citation context not shown here]

L. Babai, N. Nisan, and M. Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. J. Comput. Syst. Sci., 45:204--232, 1992.

No context found.

L. Babai, N. Nisan, M. Szegedy, Multiparty protocols, pseudorandom generators for Logspace, and time-space trade-os. J. Comp. Sys. Sci. 45 (1992), 204-232.

....question in complexity theory. Despite much effort very little is known. In this paper we consider this question when the complexity measured is space. Is randomized space(S) stronger than deterministic space(S) While several nontrivial deterministic simulations of randomized space are known [BNS, N1, N2], this question is still completely open. No simulation of randomized space(S) is known which uses less than O(S 2 ) deterministic space, a simulation which can be achieved by Savitch s theorem [S] Indeed, from Savitch s proof it follows that a language accepted by a randomized space(S) ....

L. Babai, N. Nisan, and M. Szegedy, Multiparty Protocols, Pseudorandom Generators for Logspace, and Time-Space Tradeoffs, J. Comp. Syst. and Sci. 45(2) (1992), pp. 204-232.

.... [14] Raz and Wigderson [19] Boolean decision trees (Hajnal, Maass, and Tur an [13] combinatorial optimization (Yannakakis [23] VLSI (Aho, Ullman and Yannakakis [3] Lipton and Sedgewick [16] Mehlhorn and Schmidt [18] Yao [25] and pseudorandom number generators (Babai, Nisan, and Szegedy [5]) Nearly all previous work on the communication complexity of various problems has focused on their communication requirements alone, in the absence of any limitations on the individual processors. Lam, Tiwari, and Tompa [15] initiated the study of communication complexity when the processors ....

L. Babai, N. Nisan, and M. Szegedy, Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs, Journal of Computer and System Sciences, 45 (1992), pp. 204--232.

....question in complexity theory. Despite much effort very little is known. In this paper we consider this question when the complexity measured is space. Is randomized space(S) stronger than deterministic space(S) While several nontrivial deterministic simulations of randomized space are known [2, 15, 16], this question is still completely open. No simulation of randomized space(S) is known which uses less than O(S 2 ) deterministic space, a simulation which can be achieved by Savitch s theorem [17] Indeed, from Savitch s proof it follows that a language accepted by a randomized space(S) ....

L. Babai, N. Nisan, and M. Szegedy, Multiparty Protocols, Pseudorandom Generators for Logspace, and Time-Space Tradeoffs, J. Comp. Syst. and Sci. 45(2) (1992), pp. 204-232.

....in that vertex. Definition 6.3. A string # # 1, 2, r # is called an r universal sequence if for every graph G with at most r vertices and any r labeling of G a walk according to # visits all the vertices of G regardless of the starting vertex. By following the proofs of [AKL 79] [BNS92], and [Nis92] it is not di#cult to see that the construction of [Nis92] yields an r universal sequence of length r O(log r) in our general sense. We need only the following two properties. Theorem 6.4 (see [Nis92] An r universal sequence of length l = r O(log r) can be generated by an EREW ....

<F3.742e+05> L. Babai, N. Nisan, and M.<F3.822e+05> Szegedy,<F3.856e+05> Multiparty protocols, pseudorandom generators for logspace, and time-space<F3.822e+05> trade-o#s, J. Comput. System Sci., 45 (1992), pp. 204--232.

No context found.

L. Babai, N. Nisan, M. Szegedy. Multiparty protocols, pseudorandom generators for Logspace, and time-space trade-offs. Journal of Comput. Syst. Sci., vol. 45 (1992), pp. 204-232.

No context found.

L. Babai, N. Nisan, and M. Szegedy, Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. J. Comput. System Sci. 45 (1992), 204--232.

No context found.

L. Babai, N. Nisan and M. Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. Journal of Computer and System Sciences, 45:204--232, 1992.

No context found.

L. Babai, N. Nisan, and M. Szegedy, Multiparty protocols, pseudorandom generators for logspace, and time--space trade-offs, Journal of Computer and System Sciences, 45 (1992), pp. 204--232.

No context found.

L. Babai, N. Nisan, M. Szegedy, Multiparty protocols, Pseudorandom Generators for Logspace, and Time-Space Trade-os, Journal of Computer and System Sciences, vol.45, 1992, pp. 204-232.

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