Search Results - Boolean function complexity theory

The Error Linear Complexity Spectrum as a Cryptographic Criterion of Boolean Functions by Limniotis, Konstantinos, Kolokotronis, Nicholas

“… to be modified per period increases. In this paper, via defining an association between <inline-formula> <tex-math notation="LaTeX">2^{n} </tex-math></inline-formula>-periodic binary sequences and Boolean functions…”
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Monomial Boolean functions with large high-order nonlinearities by Gao, Jinjie, Kan, Haibin, Li, Yuan, Xu, Jiahua, Wang, Qichun

“…Exhibiting an explicit Boolean function with a large high-order nonlinearity is an important problem in cryptography, coding theory, and computational complexity…”
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Toward a theory of one -way functions via gate complexity of Boolean functions by Interlando, J Carmelo

“… (or circuit) complexity of Boolean functions. The computational security of public-key cryptographic systems depends fundamentally on trapdoor one-way functions…”
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Boolean functional synthesis: hardness and practical algorithms by Akshay, S., Chakraborty, Supratik, Goel, Shubham, Kulal, Sumith, Shah, Shetal

“… In trying to understand this behaviour, we show that unless some hard conjectures in complexity theory are falsified, Boolean functional synthesis must generate large Skolem functions in the worst-case…”
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A Note on the LogRank Conjecture in Communication Complexity by Grolmusz, Vince

“…The LogRank conjecture of Lovász and Saks (1988) is the most famous open problem in communication complexity theory…”
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Boolean Functions of Low Polynomial Degree for Quantum Query Complexity Theory by Freivalds, R., Garkaje, L.

“… Unfortunately, it is a well-known problem to construct such functions. The best separation between these two complexity measures of a Boolean function was exhibited by Ambai- nis [5…”
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Almost-natural proofs by Chow, Timothy Y.

“… ) that exclude P / poly . This famous result is widely regarded as a serious barrier to proving strong lower bounds in circuit complexity theory, because virtually all Boolean function properties used in existing lower bound…”
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The Complexity of Deciding if a Boolean Function Can Be Computed by Circuits over a Restricted Basis by Vollmer, Heribert

“…We study the complexity of the following algorithmic problem: Given a Boolean function f and a finite set of Boolean functions B , decide if there is a circuit with basis B that computes  f…”
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AN ABSTRACT COMPLEXITY THEORY FOR BOOLEAN FUNCTIONS by KOOB, GARY MICHAEL

“…Traditional theories measure the complexity of a function as a lower bound on the cost of its implementation…”
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Sensitivity as a Complexity Measure for Sequence Classification Tasks by Hahn, Michael, Jurafsky, Dan, Futrell, Richard

“…We introduce a theoretical framework for understanding and predicting the complexity of sequence classification tasks, using a novel extension of the theory of Boolean function sensitivity…”
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On covering graphs by complete bipartite subgraphs by Jukna, S., Kulikov, A.S.

“… We also formulate several open problems about covering problems for graphs whose solution would have important consequences in the complexity theory of boolean…”
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Interplay between resiliency and polynomial degree — Recursive amplification, higher order sensitivity and beyond by Maitra, Subhamoy, Mukherjee, Chandra Sekhar, Stănică, Pantelimon, Tang, Deng

“…Boolean functions are important primitives in different domains of cryptology, complexity and coding theory, and far beyond in different areas of science and technology…”
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Sensitivity versus block sensitivity of Boolean functions by Virza, Madars

“…Determining the maximal separation between sensitivity and block sensitivity of Boolean functions is of interest for computational complexity theory…”
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Separation results for boolean function classes by Biswas, Aniruddha, Sarkar, Palash

“… class. In particular, we show (almost) separation of several classes of Boolean functions which have been studied in coding theory and cryptography from classes which have been…”
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Measuring Area-Complexity Using Boolean Difference by Kagliwal, A., Balachandran, S.

“… In this paper, we propose a novel area-complexity measure using the theory of Boolean difference and Taylor expansion for Boolean functions…”
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Block sensitivity of minterm-transitive functions by Drucker, Andrew

“…Boolean functions with a high degree of symmetry are interesting from a complexity theory perspective…”
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Necessary and sufficient conditions for Boolean satisfiability by Margaryan, Stepan G

“… The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to transform any Boolean function in conjunctive normal form into a specific form…”
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Certificate complexity of elementary symmetric Boolean functions by Zhang, Jing, Li, Yuan

“… Certificate complexity is an important combinatorial measure of Boolean function complexity…”
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Lower Bounds on Stabilizer Rank by Peleg, Shir, Shpilka, Amir, Ben Lee Volk

“…The stabilizer rank of a quantum state \(\psi\) is the minimal \(r\) such that \(\left| \psi \right \rangle = \sum_{j=1}^r c_j \left|\varphi_j \right\rangle\)…”
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Distributed Pinning Set Stabilization of Large-Scale Boolean Networks by Zhu, Shiyong, Lu, Jianquan, Sun, Liangjie, Cao, Jinde

“…In this article, we design the distributed pinning controllers to globally stabilize a Boolean network (BN…”
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