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In this paper we study a nonuniform notion of one-wayness based on circuit complexity. ... They show that a family of one-way one-to-one functions exists if and only if the nonuniform versions of the complexity classes P and UP are not equal, and that a family of one-way one-to-one and onto ...doi:10.1016/0890-5401(87)90022-8 fatcat:b3p6uastine7nmhipvy4cwoqle
Lecture Notes in Computer Science
In this paper we study a nonuniform notion of one-wayness based on circuit complexity. ... They show that a family of one-way one-to-one functions exists if and only if the nonuniform versions of the complexity classes P and UP are not equal, and that a family of one-way one-to-one and onto ...doi:10.1007/3-540-16486-3_89 fatcat:2wixutunrjf2no27fku3cltg6m
We explore the possibility of basing one-way functions on the average-case hardness of the fundamental Minimum Circuit Size Problem (MCSP[s]), which asks whether a Boolean function on n bits specified ... We show that under the Universality Conjecture, the following are equivalent: One-way functions exist; Natural proofs useful against sub-exponential size circuits do not exist; Learning polynomial-size ... Are one-way functions equivalent to auxiliary-input one-way functions? One-way functions are also relevant to proof complexity. ...doi:10.4230/lipics.itcs.2020.68 dblp:conf/innovations/Santhanam20 fatcat:pgatorc5k5hlrknytijhfgjufy
In the field of cryptography, in particular, one-way functions play an important role; several candidates for one-way functions have been proposed and used there. ... (J-TOKYTE-C) On one-way functions. Combinatorics, computing and complexity (Tianjing and Beijing, 1988), 98-131, Math. Appl. (Chinese Ser.), 1, Kluwer Acad. Publ., Dordrecht, 1989. ...
International Journal of Physical Sciences
Since the analysis of complex circuits with resistors, inductors and capacitors for sinusoidal entry types is time consuming, the sinusoidal analysis by phasors is a simple way to analyze such circuits ... Phasors provide a simple way to analyze sinusoidally excited linear circuits. Solutions of those circuits would be undoable otherwise. ... CONCLUSIONS In this article, we present another way, from linear algebra, that do not require the Euler identity, to show the relationship between the sinusoidal function, complex numbers and plane . ...doi:10.5897/ijps2016.4547 fatcat:wp7mpihcvfcjvg724a7il7pi4y
We describe and motivate a proposed new approach to lowerbounding the circuit complexity of boolean functions, based on a new formalization of "patterns" as elements of a special basis of the vector space ... We prove that a "pattern basis" with certain properties would lead to a useful complexity formula of a specific form, and speculate on how to find such a basis. ... Acknowledgements This paper wouldn't exist without the excellent expository blogs of Scott Aaronson and Timothy Gowers, which introduced me to the status of circuit complexity and to the "natural proofs ...arXiv:1606.05331v1 fatcat:s32muoyd6zau7fj6g2dmwjqcyy
Lecture Notes in Computer Science
We review the past ten years in computational complexity theory by focusing on ten theorems that the author enjoyed the most. ... We use each of the theorems as a springboard to discuss work done in various areas of complexity theory. ... Lokam,Dieter Van Melkebeek and Sophie Laplante for their comments and help on this paper. ...doi:10.1007/3-540-58715-2_130 fatcat:oqj4nco6ozaxpclwtipoor2egi
f0; 1g, with which any small circuit disagrees on (1 0 )=2 fraction of the input, into a harder function f 0 , with which any small circuit disagrees on (1 0 k )=2 fraction of the input. ... First, we show that such hardness amplification, when carried out in some black-box way, must require a high complexity. ... Viola for many helpful discussions and anonymous referees for their useful comments. ...doi:10.1109/tit.2008.928988 fatcat:7niutgi45vdwhcuhg66cr2lgkq
Cryptography and Security in Computing
Feebly secure one-way functions We want the size of circuits breaking our family of trapdoor functions to be larger than the size of circuits that perform encoding. ... This argument suffices for Hiltgen's feebly one-wayness result for the square matrix A −1 :fi rst we apply the first part of Proposition 6 and see that every output has complexity at least n 2 − 1, and ...doi:10.5772/37084 fatcat:vuodckqbevendfw5bff45z4rlm
All the main methods known for proving lower bounds on the monotone complexity of Boolean functions fail to work in their present form for slice functions. ... By a result of Berkowitz (1982) , the monotone circuit complexity of slice functions cannot be much larger than the circuit (combinational) complexity of these functions for arbitrary complete bases. ... Acknowledgment I like to thank Les Valiant, Mike Paterson, Riidiger Reischuk, and Friedhelm Meyer auf der Heide for valuable discussions about this paper. ...doi:10.1016/0304-3975(85)90209-9 fatcat:zmdf2oxlcngf5gg4htxa4s3qui
The latter method is covered in a published article and will not be presented Roots on the s axis: Regular RL and RC circuits have roots on the s axis • Complex conjugate roots: Typical RLC circuits, and ... RL and RC circuits with feedback generally have their transfer functions with complex roots • Roots on the jw axis: Oscillators, LC and tuned amplifiers have their roots on the jw axis by design Bode ...doi:10.1109/lascas.2015.7250464 dblp:conf/lascas/Hashemian15 fatcat:zcqydfe2anapdcefzs5zevwmby
Automation and Remote Control
of circuits, realizing the same output functions, for which the histogram was constructed was between one and two hundred, Histograms were plotted after the first hundred and then after each twenty circuits ... 4. g a(fi*) = - gif *e xj) isa relative estimate of the complexity of a Boolean function, This method of evaluation is a particular case of the relative estimate of complexity of Boolean functions, considered ...
Functional labels provide a simple but very reusable way for defining the functionality of a system and for making use of that knowledge. ... Unlike more complex functional representation schemes, these labels can be efficiently linked to a behavioral simulator to interpret the simulation in a way that is meaningful to the user. ... Acknowledgements This work has been carried out on the UK EPSRC funded projects "Flame" and "Aquavit", with the cooperation of Jaguar Cars Ltd, Ford Motor Company Ltd, the Motor Industry Research Association ...doi:10.1016/s0954-1810(97)10013-9 fatcat:tz2gsg4tp5av5kug7uclgy3zu4
Among the most common units, the so called inverted IMPLIES (N-Implies) appears to be one of the most important elements along with the NOT or AND functions. ... Biological systems perform computations at multiple scales and they do so in a robust way. ... Acknowledgments We thank Alfred Borden and the members of the Complex Systems Lab for useful discussions. This work has been supported by and EU ERC Advanced Grant, the James S. ...doi:10.1371/journal.pone.0081248 pmid:24586222 pmcid:PMC3929274 fatcat:im6l6cmedrby3oqczy24uwa7wa
By probing how activity patterns in different types of neurons and circuits contribute to behavior, these tools can help inform mechanistic models of brain function and explain the roles of distinct circuit ... Thankfully, optogenetics and other recently developed circuit manipulation tools are making it possible to control the activity of circuits and cell types with increasing specificity, something that has ... Acknowledgments We thank Sean Escola, James Fitzgerald, Grigori Guitchounts, Johannes Letzkus, Philip Tovote and the whole Ölveczky lab for helpful comments on the manuscript. ...doi:10.1016/j.conb.2018.01.004 pmid:29414070 pmcid:PMC5957484 fatcat:uxdbpg4hwzbyxhpdctg7z5jgme
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