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The study of monotonicity and negation complexity for Boolean functions has been prevalent in complexity theory as well as in computational learning theory, but little attention has been given to it in the cryptographic context. Recently, Goldreich and Izsak (2012) have initiated a study of whether cryptographic primitives can be monotone, and showed that… (More)

We show the following reductions from the learning with errors problem (LWE) to the learning with rounding problem (LWR): (1) Learning the secret and (2) distinguishing samples from random strings is at least as hard for LWR as it is for LWE for efficient algorithms if the number of samples is no larger than O(q/Bp), where q is the LWR modulus, p is the… (More)

We consider the problem of extracting entropy by sparse transformations, namely functions with a small number of overall input-output dependencies. In contrast to previous works, we seek extractors for essentially all the entropy without any assumption on the underlying distribution beyond a min-entropy requirement. We give two simple constructions of… (More)

Rational proofs, recently introduced by Azar and Micali (STOC 2012), are a variant of interactive proofs in which the prover is neither honest nor malicious, but rather rational. The advantage of rational proofs over their classical counterparts is that they allow for extremely low communication and verification time. Azar and Micali demonstrated their… (More)

We give an efficient structural decomposition theorem for formulas that depends on their negation complexity and demonstrate its power with the following applications. We prove that every formula that contains t negation gates can be shrunk using a random restriction to a formula of size O(t) with the shrinkage exponent of monotone formulas. As a result,… (More)

Rational proofs, introduced by Azar and Micali (STOC 2012) are a variant of interactive proofs in which the prover is neither honest nor malicious, but rather rational. The advantage of rational proofs over their classical counterparts is that they allow for extremely low communication and verification time. In recent work, Guo et al. (ITCS 2014)… (More)

- Xiangke Duan, Yunsong Li, Qinglin Du, Qinqin Huang, Siyao Guo, Mengmeng Xu +3 others
- Scientific reports
- 2016

Bacterial persisters, usually slow-growing, non-replicating cells highly tolerant to antibiotics, play a crucial role contributing to the recalcitrance of chronic infections and treatment failure. Understanding the molecular mechanism of persister cells formation and maintenance would obviously inspire the discovery of new antibiotics. The significant… (More)

A Boolean k-monotone function defined over a finite poset domain D alternates between the values 0 and 1 at most k times on any ascending chain in D. Therefore, k-monotone functions are natural generalizations of the classical monotone functions, which are the 1-monotone functions. Motivated by the recent interest in k-monotone functions in the context of… (More)

We prove that for every n and 1 < t < n any tout of -n threshold secret sharing scheme for one-bit secrets requires share size log(t + 1). Our bound is tight when t = n − 1 and n is a prime power. In 1990 Kilian and Nisan proved the incomparable bound log(n − t + 2). Taken together, the two bounds imply that the share size of Shamir's secret sharing scheme… (More)

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