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590
A 2.5nlower bound on the combinational complexity of Boolean functions
 SIAM Journal of Computing
, 1977
"... Abstract. Consider the combinational complexity L(f) of Boolean functions over the basis fl={]’l]’: {0, 1}2>{0, 1}}. A new method for proving linear lower bounds of size 2n is presented. Combining it with methods presented in Savage 13, (1974)] and Schnorr 18, (1974)], we establish for a specia ..."
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Cited by 14 (0 self)
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Abstract. Consider the combinational complexity L(f) of Boolean functions over the basis fl={]’l]’: {0, 1}2>{0, 1}}. A new method for proving linear lower bounds of size 2n is presented. Combining it with methods presented in Savage 13, (1974)] and Schnorr 18, (1974)], we establish for a
Algebraic methods in the theory of lower bounds for boolean circuit complexity
 IN PROCEEDINGS OF THE 19TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, STOC ’87
, 1987
"... We use algebraic methods to get lower bounds for complexity of different functions based on constant depth unbounded fanin circuits with the given set of basic operations. In particular, we prove that depth k circuits with gates NOT, OR and MOD, where p is a prime require Ezp(O(n’)) gates to calcu ..."
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Cited by 329 (1 self)
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We use algebraic methods to get lower bounds for complexity of different functions based on constant depth unbounded fanin circuits with the given set of basic operations. In particular, we prove that depth k circuits with gates NOT, OR and MOD, where p is a prime require Ezp(O(n’)) gates
The monotone circuit complexity of Boolean functions
 COMBINATORICA
, 1987
"... Recently, Razborov obtained superpolynomial lower bounds for monotone circuits that lect cliques in graphs. In particular, Razborov showed that detecting cliques of size s in a graph dh m vertices requires monotone circuits of size.Q(m'/(log m) ~') for fixed s, and size rn ao°~') for ..."
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Cited by 144 (2 self)
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cliques of size s requires 'm'/(log m)') AND gates. We show that even a very rough approximation of the maximum clique e of a graph requires superpolynomial size monotone circuits, and give lower bounds for some net Boolean functions. Our best lower bound fi~r an NP function of n variables
An Explicit Lower Bound of 5n − o(n) for Boolean Circuits
 Proc. of MFCF
, 2002
"... Abstract. We prove a lower bound of 5n − o(n) for the circuit complexity of an explicit (constructible in deterministic polynomial time) Boolean function, over the basis U2. That is, we obtain a lower bound of 5n − o(n) for the number of {and, or} gates needed to compute a certain Boolean function, ..."
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Cited by 11 (1 self)
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Abstract. We prove a lower bound of 5n − o(n) for the circuit complexity of an explicit (constructible in deterministic polynomial time) Boolean function, over the basis U2. That is, we obtain a lower bound of 5n − o(n) for the number of {and, or} gates needed to compute a certain Boolean function
Explicit Lower Bound Of 4.5n  o(n) For Boolean Circuits
 Proc. of 33rd STOC (2001
, 2001
"... We prove a lower bound of 4:5n o(n) for the circuit complexity of an explicit Boolean function (that is, a function constructible in deterministic polynomial time), over the basis U2 . That is, we obtain a lower bound of 4:5n o(n) for the number of fand; org gates needed to compute a certain Boolea ..."
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Cited by 8 (0 self)
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We prove a lower bound of 4:5n o(n) for the circuit complexity of an explicit Boolean function (that is, a function constructible in deterministic polynomial time), over the basis U2 . That is, we obtain a lower bound of 4:5n o(n) for the number of fand; org gates needed to compute a certain
Approximation of Boolean Functions by Combinatorial Rectangles
 Electr. Coll. on Comp. Compl
, 2000
"... This paper deals with the number of monochromatic combinatorial rectangles required to approximate a Boolean function on a constant fraction of all inputs, where each rectangle may be defined with respect to its own partition of the input variables. The main result of the paper is that the number of ..."
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Cited by 2 (2 self)
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This paper deals with the number of monochromatic combinatorial rectangles required to approximate a Boolean function on a constant fraction of all inputs, where each rectangle may be defined with respect to its own partition of the input variables. The main result of the paper is that the number
A 4n LOWER BOUND ON THE COMBINATIONAL COMPLEXITY OVER . . . Of Certain Symmetric boolean functions
"... A simple and easy to check property of a symmetric boolean function is shown to imply a 4n 9 lower bound on the circuit complexity of the function over U 2 = B 2 f; g. Among the functions to which this lower bound applies are the modular functions MOD k (n) for any fixed k 3 (MOD k (n) is the ..."
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A simple and easy to check property of a symmetric boolean function is shown to imply a 4n 9 lower bound on the circuit complexity of the function over U 2 = B 2 f; g. Among the functions to which this lower bound applies are the modular functions MOD k (n) for any fixed k 3 (MOD k (n
A 5n − o(n) Lower Bound on the Circuit Size over U2 of a Linear Boolean Function
"... We give a simple proof of a 5n − o(n) lower bound on the log n×n circuit size over U2 of a linear function f(x) = Ax where A ∈ {0, 1} (here, U2 is the set of all Boolean binary functions except for parity and its complement). ..."
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Cited by 1 (0 self)
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We give a simple proof of a 5n − o(n) lower bound on the log n×n circuit size over U2 of a linear function f(x) = Ax where A ∈ {0, 1} (here, U2 is the set of all Boolean binary functions except for parity and its complement).
Circuit Complexity and Multiplicative Complexity of Boolean Functions
 IN: PROCEEDINGS OF COMPUTABILITY IN EUROPE (CIE). VOLUME 6158 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2010
"... In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key ide ..."
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Cited by 2 (0 self)
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In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key
On The Multiplicative Complexity of Boolean Functions over the Basis ...
, 1998
"... . The multiplicative complexity c(f) of a Boolean function f is the minimum number of AND gates in a circuit representing f which employs only AND, XOR and NOT gates. A constructive upper bound, c(f) = 2 n 2 +1 \Gamma n=2 \Gamma 2, for any Boolean function f on n variables (n even) is given. A c ..."
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Cited by 25 (9 self)
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. The multiplicative complexity c(f) of a Boolean function f is the minimum number of AND gates in a circuit representing f which employs only AND, XOR and NOT gates. A constructive upper bound, c(f) = 2 n 2 +1 \Gamma n=2 \Gamma 2, for any Boolean function f on n variables (n even) is given. A
Results 1  10
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590