منابع مشابه
Superpolynomial Lower Bounds for Monotone Span Programs
In this paper we obtain the first superpolynomial lower bounds for monotone span programs computing explicit functions. The best previous lower bound was Ω(n) by Beimel, Gál, Paterson [BGP]; our proof exploits a general combinatorial lower bound criterion from that paper. Our lower bounds are based on an analysis of Paley-type bipartite graphs via Weil’s character sum estimates. We prove an n n...
متن کاملSuperpolynomial Lower Bounds for Monotone Span Programs 1
In this paper we obtain the rst superpolynomial lower bounds for monotone span programs computing explicit functions. The best previous lower bound was (n5=2) by Beimel, G al, Paterson [BGP]; our proof exploits a general combinatorial lower bound criterion from that paper. Our lower bounds are based on an analysis of Paley-type bipartite graphs via Weil's character sum estimates. We prove an n ...
متن کاملNew Monotone Span Programs from Old
In this paper we provide several known and one new constructions of new linear secret sharing schemes (LSSS) from existing ones. This constructions are well-suited for didactic purposes, which is a main goal of this paper. It is well known that LSSS are in one-to-one correspondence with monotone span programs (MSPs). MSPs introduced by Karchmer and Wigderson, can be viewed as a linear algebra m...
متن کاملLower Bounds for Monotone Counting Circuits
A {+,×}-circuit counts a given multivariate polynomial f , if its values on 0-1 inputs are the same as those of f ; on other inputs the circuit may output arbitrary values. Such a circuit counts the number of monomials of f evaluated to 1 by a given 0-1 input vector (with multiplicities given by their coefficients). A circuit decides f if it has the same 0-1 roots as f . We first show that some...
متن کاملOn the Size of Monotone Span Programs
Span programs provide a linear algebraic model of computation. Monotone span programs (MSP) correspond to linear secret sharing schemes. This paper studies the properties of monotone span programs related to their size. Using the results of van Dijk (connecting codes and MSPs) and a construction for a dual monotone span program proposed by Cramer and Fehr we prove a non-trivial upper bound for ...
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ژورنال
عنوان ژورنال: BRICS Report Series
سال: 1994
ISSN: 1601-5355,0909-0878
DOI: 10.7146/brics.v1i46.21596