Alon, N., and Maass, W. Meanders, Ramsey theory and lower bounds for branching programs. In Proc. 27-th Annual Symp. on Foundations of Computer Science (FOCS) (Toronto, ON.) (1986), pp. 410-417.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....threshold functions. For bounded width branching programs, computing any member of a large class of symmetric Boolean functions## n log n log log n) lower bound was obtained in [2] but for this they could not use the help of Ramsey type methods. It was further improved to ## n log n) in [24] and [12] independently, the later again using Ramsey methods. Alon and Maass [12, 13] have several results about lower bounds for the length of branching programs of various symmetric functions, or lower bounds for the time space complexity trado# in a general input oblivious sequential model of ....

....of a large class of symmetric Boolean functions## n log n log log n) lower bound was obtained in [2] but for this they could not use the help of Ramsey type methods. It was further improved to ## n log n) in [24] and [12] independently, the later again using Ramsey methods. Alon and Maass [12, 13] have several results about lower bounds for the length of branching programs of various symmetric functions, or lower bounds for the time space complexity trado# in a general input oblivious sequential model of computation of certain functions, using the following Ramsey theoretic lemma stated ....

N. Alon and W. Maass, Meanders, Ramsey Theory and lower bounds for branching programs, Proc. 27-th Annual Symp. on Foundations of Computer Science (FOCS), Toronto (1986), 410--417. 26

....program is called oblivious if the node set can be partitioned into levels such that edges lead from lower to higher levels and all inner nodes of one level are labeled by the same variable. Exponential lower bounds for oblivious branching programs of restricted depth have been proved by Alon and Maass (1986), Babai, Nisan, and Szegedy (1992) Krause (1991) and Krause and Waack (1991) The method of Babai, Nisan, and Szegedy works up to depth o(n log 2 n) but one cannot prove for explicitly defined Boolean functions that they can be represented in polynomial size in depth (k 1)n but not in depth ....

Alon, N. and Maass, W. (1986). Meanders, Ramsey theory and lower bounds for branching programs. In 22nd Symp. on Found. of Computer Science, 410--417.

..... Since lower bounds for certain weak automata are known, this yields a contradiction. For example, the proof system regular resolution corresponds directly to the class of read once branching programs [Kra95] Thus, the known technology for proving lower bounds on read once branching programs ( AM86, SS93] can be brought to bear on lower bounds for resolution [RWY97] Our idea is to reverse this correspondence: proof system # automata class. In our case we plan to look at the reverse correspondence: automata class # proof system. Roughly, in a natural way given an class of automata we ....

....clauses we consider are fsa type formulas: these are simply formulas that can be computed easily by an fsa for any ordering of their variables. The lower bound for oblivious regular resolution is implied by a lower bound for oblivious branching programs, that uses a technique of Alon and Maass [AM86] 2 Preliminaries Many results have been established recently for restricted computation models and especially for branching programs, but proving lower bounds for general unrestricted models seems to be far beyond current knowledge. Branching programs are graph representations of discrete ....

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Noga Alon and Wolfgang Maass. Meanders, Ramsey theory and lower bounds for branching programs. In 27th Symposium on Foundations of Computer Science, pages 410--417. IEEE, 1986.

....by analyzing the communication between various parts of the computational device. This concerns area time tradeoffs for VLSI computations ( 1] 9] time space tradeoffs for Turing machines, width length tradeoffs for oblivious and usual branching programs and Omega Gammad 189 hing programs ([2], 12] Moreover, lower bounds on the depth of monotone circuits ( 16] structural results in designing pseudorandom sequences ( 4] and lower bounds on the size of special threshold circuits of depth 3 ( 8] should be mentioned in this connection. Babai, Frankl, and Simon in [3] introduced the ....

N. Alon, W. Maass, Meanders, Ramsey theory and lower bounds for branching programs, Journ. of Comp. and System Sciences 37(1988), pp. 118--129.

....this is of course much weaker than what we would like to prove, the graph leveling structure used by that proof may be relevant to proving the conjecture. Also note that in the nonmonotone case, the best lower bounds for the length of BWBP programs for explicit functions are Omega Gamma n lg n) [6, 8]. 4.1 There is no Monotone Barrington Gadget Our result here states that there is no monotone gadget (of any length or width) like Barrington s gadget composed of four 5 cycles [9] Note this is not an asymptotic result, but rather a statement of impossibility. We need a few definitions to state ....

N. Alon and W. Maass. Meanders, Ramsey theory and lower bounds for branching programs. In 27 th Annual Symposium on Foundations of Computer Science, pages 410--417. IEEE, 1986.

....program is called oblivious, if the node set can be partitioned into levels such that edges are leading from lower to higher levels and all inner nodes of one level are labeled by the same variable. Exponential lower bounds for oblivious branching programs of restricted depth have been proved by Alon and Maass (1986), Babai, Nisan and Szegedy (1992) Krause (1991) and Krause and Waack (1991) The method of Babai, Nisan and Szegedy works up to depth o(n log 2 n) Again we do not obtain tight hierarchies. Besides this complexity theoretic viewpoint people have used branching programs in applications. In ....

Alon, N. and Maass, W. (1986). Meanders, Ramsey theory and lower bounds for branching programs. In 22nd Symp. on Found. of Computer Science, 410--417.

....of complexity theory were answered by reducing them to several kinds of communication games. Among others, this regards time area tradeoffs for VLSI circuits [1] 10] time space tradeoffs for Turing machines, width length tradeoffs for oblivious and usual Omega Gammaual 1 hing programs ([2], 4] branching programs of bounded alternation [14] and threshold circuits of depth 2 [11] and depth 3 [7] The graph connectivity problem for undirected graphs UCONN = UCONN n(n Gamma1) n2IN in distributed form can be formulated as follows. Assume that we are given two not necessarily ....

N. Alon, W. Maass, Meanders, Ramsey theory and lower bounds for branching programs, Journal of Computer and System Sciences 37(1988), pp. 118--129.

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Alon, N., and Maass, W. Meanders, Ramsey theory and lower bounds for branching programs. In Proc. 27-th Annual Symp. on Foundations of Computer Science (FOCS) (Toronto, ON.) (1986), pp. 410-417.

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