A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Filters
Dimension of Projections in Boolean Functions
1998
SIAM Journal on Discrete Mathematics
Preserved Fulltext
We study monochromatic projections in 2-colorings of an n-dimensional Boolean cube. We also study the dimension of the largest projection contained in a set specified by its density. ...
We also prove almost tight upper and lower bounds on the dimension of monochromatic projections in arbitrary Boolean functions. ...
We also obtain bounds on the dimension of the largest monochromatic projections in arbitrary Boolean functions. ...
doi:10.1137/s0895480197318313
fatcat:jrwu67wpifh73pz4sgikqmhbaa
Boolean Functions, Projection Operators, and Quantum Error Correcting Codes
2008
IEEE Transactions on Information Theory
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. ...
The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the design of both additive and non-additive quantum error correcting codes. ...
ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for many suggestions that improved this paper and for bringing the work of Danielson [12] to their attention. ...
doi:10.1109/tit.2008.917720
fatcat:n6ewbvhtgzbcxgr2gdtf6t6oki
Exponential lower bounds for depth 3 Boolean circuits
1997
Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC '97
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
~: = ~1) of dimension at least w. ...
We consider the class ~k of unbounded fan-in depth-3 boolean circuits, for which the bottom fan-in is limited by k and thetop gateis an OR. ...
Acknowledgments: The authorswould like to thankJohan Hktad for pointing out an error in the example in section 2. ...
doi:10.1145/258533.258556
dblp:conf/stoc/PaturiSZ97
fatcat:hp7xra5sw5c7dcx447gbkndaxe
The construction and weight distributions of all projective binary linear codes
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Boolean functions can be used to construct binary linear codes in many ways, and vice versa. ...
The objective of this short article is to point out a connection between the weight distributions of all projective binary linear codes and the Walsh spectra of all Boolean functions. ...
In addition, other connections between projective binary codes and Boolean functions could also be developed. ...
arXiv:2010.03184v2
fatcat:iepzzct7vfa3jllyk3d56gawrq
Exponential lower bounds for depth three Boolean circuits
2000
Computational Complexity
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We consider the class Σ k 3 of unbounded fan-in depth three Boolean circuits, for which the bottom fan-in is limited by k and the top gate is an OR. ...
1, x i = x j or x i =x j ) of dimension at least log(a/s)/log n. ...
A version of this paper appeared previously as Paturi et al. ( 1997 ) . ...
doi:10.1007/pl00001598
fatcat:7d5qcgwdyjamjfzsfp7h7b7yam
The threshold order of a Boolean function
1991
Discrete Applied Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
It is also shown that a Boolean function is a threshold function of order at least m if some sequence of "contractions" and "projections" of it to a (generally) lower dimensional space is a threshold function ...
We have used such functions in the problem of extrapolating partially defined Boolean functions. ...
Let f(x) be an n-dimensional
Boolean function,
and let Tf= {x E B" (f(x) = 1) be
the set of sisting of a polynomial
pseudo-Boolean
function of degree m, determined
by the
vector w of dimension ...
doi:10.1016/0166-218x(91)90032-r
fatcat:xlaly3sonbbgdcwb6hly3cqbnm
Classifying bent functions by their Cayley graphs
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
In 1999 Bernasconi and Codenotti noted that the Cayley graph of a bent function is strongly regular. ...
SageMath scripts and CoCalc worksheets are used to compute and display some of these relationships, for bent functions up to dimension 8. ...
The algorithm uses 8 S-boxes, each of which consists of 32 Boolean bent functions in 8 dimensions, with degree 4, making 256 bent functions in total. ...
arXiv:1705.04507v6
fatcat:rblk4oisyfazjp56qkatxrpdvq
A New Abstract Combinatorial Dimension for Exact Learning via Queries
2002
Journal of computer and system sciences (Print)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We present a characterization of those Boolean function classes learnable in this abstract model, in terms of a new combinatorial notion that we introduce, the abstract identi cation dimension. ...
currently known to characterize learning in these models, such as strong consistency dimension, extended teaching dimension, and certi cate size. ...
A Boolean function of arity n is a function from f0; 1g n ! f0; 1g. The set of all Boolean functions is denoted by B n . An element x of f0; 1g n is called an assignment. ...
doi:10.1006/jcss.2001.1794
fatcat:3maos6rua5gfnaolgxylnfth7i
Characterization and Lower Bounds for Branching Program Size using Projective Dimension
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Motivated by the argument in (Pudlák, Rödl 1992), we define two variants of projective dimension - projective dimension with intersection dimension 1 (denoted by upd(G)) and bitwise decomposable projective ...
We show that there exist a Boolean function f (on n bits) for which the gap between the projective dimension and size of the optimal branching program computing f (denoted by bpsize(f)), is 2^Ω(n). ...
5.1 follows from Remark 1.3 in [8] . ...
arXiv:1604.07200v2
fatcat:56n3dlpjpbggbdhvnv7zyjxiuq
Software system for solving multi-scale optimization problems
[chapter]
1996
System Modelling and Optimization
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
The objective F(B, D, X) is some quality index, representing the ability of the system to perform its functions. B E Bn is the vector of Boolean variables representing the system structure. ...
X E Rk is the vector of continuous variables representing the physical characteristics of the subsystems (mass, power consumption, etc.). 2) Planning of optimal sequence of an industrial projects' implementation ...
leads to the loss of useful properties of the objective function (monotonicity, convexity, etc.), -considerable growth of problem dimension in comparison with the dimension of an initial problem, -existence ...
doi:10.1007/978-0-387-34897-1_60
fatcat:zzk2hwbzcnbhfed4wvb6wutpmm
Separability is not the best goal for machine learning
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
For classification of difficult Boolean problems, such as the parity problem, linear projection combined with is sufficient and provides a powerful new target for learning. ...
Simple problems are 2-separable, but problems with inherent complex logic may be solved in a simple way by k-separable projections. ...
Direct search in 5-dimensional space for each of these functions is already prohibitively expensive. ...
arXiv:1807.02873v1
fatcat:mnorx7vfkrew3bxqw4v6eludia
Power Laws Variance Scaling of Boolean Random Varieties
2015
Methodology and Computing in Applied Probability
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
The exponent is equal to n k n for Boolean varieties with dimension k in the space R n : = 2 3 for Boolean ...bers in 3D, and = 1 3 for Boolean strata in 3D. ...
When working in 2D, the scaling exponent of Boolean ...bers is equal to 1 2 . ...
Figure 1 : 1 Simulation of a 2D Boolean model built on isotropic Poisson lines.
expressed as a function of the length l of the projection over the lines D ! ...
doi:10.1007/s11009-015-9464-5
fatcat:jyrasvpr2zfsthvtzw6yhla5jq
Page 7300 of Mathematical Reviews Vol. , Issue 96m
[page]
1996
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
In the special case of the latter when R = C;(U,T) is the ring of all continuous functions with compact support of a locally compact Boolean space U into a discrete indecomposable unitary ring 7, the authors ...
rings of projective generators. ...
Page 326 of Mathematical Reviews Vol. 1, Issue 11
[page]
1940
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
It is proved that the complemented modular lattices of finite dimensions which are not direct products coincide with projective geometries in the sense of Veblen and Young. ...
The terms quotient, prime quotient, transpose, projective and inde- pendent are defined. The Jordan chain condition for modu- lar lattices of finite dimensions is proved. ...
Finite-Rank Multivariate-Basis Expansions of the Resolvent Operator as a Means of Solving the Multivariable Lippmann–Schwinger Equation for Two-Particle Scattering
2014
Few-body systems
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Boolean combination of projections is explored as a means of going beyond tensor-product projection. ...
Our calculations indicate that radial function bases are very promising in the context of multivariable integral equations. ...
Tanatar on the computing facility of his research group in the Department of Physics at Bilkent University. ...
doi:10.1007/s00601-014-0887-2
fatcat:afctspzmbjhiloi6bv223y654i
« Previous
Showing results 1 — 15 out of 44,936 results