Approximate Span Programs
نویسندگان
چکیده
منابع مشابه
Approximate Span Programs
Span programs are a model of computation that have been used to design quantum algorithms, mainly in the query model. It is known that for any decision problem, there exists a span program that leads to an algorithm with optimal quantum query complexity, however finding such an algorithm is generally challenging. In this work, we consider new ways of designing quantum algorithms using span prog...
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We introduce a linear algebraic model of computation, the Span Program, and prove several upper and lower bounds on it. These results yield the following applications in complexity and cryptography: • SL ⊆ ⊕L (a weak Logspace analogue of NP ⊆ ⊕P). • The first super-linear size lower bounds on branching programs that count. • A broader class of functions which posses information-theoretic secret...
متن کاملSuperpolynomial 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 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 کاملSpan programs and quantum query algorithms
Quantum query complexity measures the number of input bits that must be read by a quantum algorithm in order to evaluate a function. Høyer et al. (2007) have generalized the adversary semidefinite program that lower-bounds quantum query complexity. By giving a matching quantum algorithm, we show that the general adversary lower bound is tight for every boolean function. The proof is based on sp...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2018
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-018-0527-1