[PDF] Top 20 Elusive Functions and Lower Bounds for Arithmetic Circuits

... sitional proof systems. We refer the reader to [3] for the many motivations (given there) for studying such tautologies. We note only that one of the original motivations for studying these tautologies was that one can ... See full document

... proving lower bounds for explicit ...enough lower bounds or PIT results for just (homogeneous) depth-4 circuits, would lead to superpolynomial lower bounds and ... See full document

... of arithmetic circuits from this latter point of ...exponential lower bounds for non-commutative arithmetic formulas (a restriction of general non-commutative arithmetic ... See full document

... and lower bounds for bounded-depth ...bounded-depth circuits implies lower bounds for such ...superpolynomial lower bounds for depth-∆ arithmetic circuits ... See full document

... [⊕] circuits by probabilistic polynomials to derive somewhat better certifying polynomials for functions with small AC 0 [⊕] ...[⊕] circuits have certifying polynomials of degree n/2 − n/(log n) O(1) ... See full document

... Corollary 1.3 suggests the following problem. Is it possible to refine the approach from [1], and to prove that the monotone circuit size complexity of k-clique is n Ω(k) for a larger range of k? In a related direction, ... See full document

... all functions we use here they are prefixed by ...strong lower bounds are known for Frege systems in these logics as well (Hrubeˇs, 2009; Jeˇr´ abek, ... See full document

... algorithms-to-lower bounds implication, proving that a similar algorithm which (for every k) runs in 2 n−ω(logn) time on all n-input n k -size circuits still implies NEXP 6⊂ ...Boolean ... See full document

... Hard Functions (MHFs) have been proposed as an answer to the growing inequality between the computational speed of general purpose CPUs and Application Specific Integrated Circuits ... See full document

... Proof overview. The proof follows a template that has been used in many results on threshold functions (see, e. g., [50, 38, 11, 20, 12, 32]). The basic idea is to divide threshold gates into one of two kinds: ... See full document

... way functions in the strongest ...establish lower bounds in cryptography ...a lower bound on the performance of traitor tracing systems satisfying a property we call IndKeys ... See full document

... Approximate arithmetic units are mainly based on the simplification of the arithmetic units ...can lower the power consumption of the flipflops and increase the speed of the ... See full document

... computing arithmetic circuits follow the secret- sharing paradigm, ...garbled circuits are an important primitive, and therefore justify study even outside the context of secure ... See full document

... Shrinking the keys in the arithmetic case. In the arithmetic case, the function f is affine, i.e., f (y, c, d) = cy + d, and we would like to encode it by the function g(y, c, d; r) = (W, ay + b) where y is ... See full document

... exponential lower bound on arbitrary extended formulations of several different ...their lower bound on the cut polytope ...such lower bounds on several other polytopes; we use his ... See full document

... The encryption algorithm in our system is similar to encryption in the hierarchical-IBE of Agrawal, Boneh, and Boyen [ABB10]. We show that this system is key-homomorphic for polynomial- size arithmetic ... See full document

... In this paper we propose the first practically efficient constructions of homomorphic MACs. The most attractive feature of our schemes is that they are efficient, simple to implement and rely on well studied assumptions. ... See full document

... of arithmetic circuits of polynomial degree and over an exponentially large finite ...for arithmetic circuits of degree d, over a finite field of order p such that d/p < ... See full document

... In this paper, we prove Levin’s type boundary behaviors for functions harmonic and admitting certain lower bounds, which extend Pan, Qiao and Deng’s inequalities for analytic functions i[r] ... See full document

... and lower bounds for the Jensen divergence for various classes of functions , including functions of bounded variation, absolutely continuous functions, Lipschitzian continuous ... See full document