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A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits
 Proceedings of the 48th FOCS: 438–448
, 2007
"... We construct an explicit polynomial f(x1,...,xn), with coefficients in {0, 1}, such that the size of any syntactically multilinear arithmetic circuit computing f is at least Ω(n 4/3 / log 2 n). The lower bound holds over any field. ..."
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Cited by 25 (12 self)
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We construct an explicit polynomial f(x1,...,xn), with coefficients in {0, 1}, such that the size of any syntactically multilinear arithmetic circuit computing f is at least Ω(n 4/3 / log 2 n). The lower bound holds over any field.
Balancing Syntactically Multilinear Arithmetic Circuits
, 2007
"... In their seminal paper, Valiant, Skyum, Berkowitz and Rackoff proved that arithmetic circuits can be balanced [VSBR]. That is, [VSBR] showed that for every arithmetic circuit Φ of size s and degree r, there exists an arithmetic circuit Ψ of size poly(r, s) and depth O(log(r) log(s)) computing the sa ..."
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Cited by 11 (4 self)
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the same polynomial. In the first part of this paper, we follow the proof of [VSBR] and show that syntactically multilinear arithmetic circuits can be balanced. That is, we show that if Φ is syntactically multilinear, then so is Ψ. Recently, [R04b] proved a superpolynomial separation between multilinear
RESOURCE TRADEOFFS IN SYNTACTICALLY MULTILINEAR ARITHMETIC CIRCUITS
"... Abstract. The class of polynomials computable by polynomial size log depth arithmetic circuits (VNC 1) is known to be computable by constant width polynomial degree circuits (VsSC 0), but whether the converse containment holds is an open problem. As a partial answer to this question, we give a const ..."
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Abstract. The class of polynomials computable by polynomial size log depth arithmetic circuits (VNC 1) is known to be computable by constant width polynomial degree circuits (VsSC 0), but whether the converse containment holds is an open problem. As a partial answer to this question, we give a
Lower bounds for syntactically multilinear algebraic branching programs
 In MFCS
, 2008
"... Abstract. It is shown that any weaklyskew circuit can be converted into a skew circuit with constant factor overhead, while preserving either syntactic or semantic multilinearity. This leads to considering syntactically multilinear algebraic branching programs (ABPs), which are defined by a natur ..."
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Cited by 9 (2 self)
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natural readonce property. A 2n/4 size lower bound is proven for ordered syntactically multilinear ABPs computing an explicitly constructed multilinear polynomial in 2n variables. Without the ordering restriction a lower bound of level Ω(n3/2 / log n) is observed, by considering a generalization of a
Lower Bounds and Separations for Constant Depth Multilinear Circuits
"... We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multilinear, if the polynomial computed by each of its gates is multilinear). We also prove a superpolynomial separation between ..."
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Cited by 39 (7 self)
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We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multilinear, if the polynomial computed by each of its gates is multilinear). We also prove a superpolynomial separation between
LowPower CMOS Digital Design
 JOURNAL OF SOLIDSTATE CIRCUITS. VOL 27, NO 4. APRIL 1992 413
, 1992
"... Motivated by emerging batteryoperated applications that demand intensive computation in portable environments, techniques are investigated which reduce power consumption in CMOS digital circuits while maintaining computational throughput. Techniques for lowpower operation are shown which use the ..."
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Cited by 570 (20 self)
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the lowest possible supply voltage coupled with architectural, logic style, circuit, and technology optimizations. An architecturalbased scaling strategy is presented which indicates that the optimum voltage is much lower than that determined by other scaling considerations. This optimum is achieved
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3499 (47 self)
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on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional
A Compositional Approach to Performance Modelling
, 1996
"... Performance modelling is concerned with the capture and analysis of the dynamic behaviour of computer and communication systems. The size and complexity of many modern systems result in large, complex models. A compositional approach decomposes the system into subsystems that are smaller and more ea ..."
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Cited by 746 (102 self)
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Performance modelling is concerned with the capture and analysis of the dynamic behaviour of computer and communication systems. The size and complexity of many modern systems result in large, complex models. A compositional approach decomposes the system into subsystems that are smaller and more
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored. AMS subject classifications: 82P10, 11Y05, 68Q10. 1 Introduction One of the first results in the mathematics of computation, which underlies the subsequent development
Results 1  10
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47,714