Filters








24 Hits in 6.8 sec

Small Space Analogues of Valiant's Classes and the Limitations of Skew Formulas

Meena Mahajan, B. V. Raghavendra Rao
2011 Computational Complexity  
We also show that exponential sums of a skew formula cannot represent the determinant polynomial.  ...  We introduce the class VL as an algebraic variant of deterministic log-space L; VL is a subclass of VP.  ...  Acknowledgments The authors are indebted to the anonymous reviewers for very detailed comments, which helped to significantly improve the presentation of the results, and for pointing out a flaw in an  ... 
doi:10.1007/s00037-011-0024-2 fatcat:bnro4engmva25nobjrwr2cxvmq

An Overview of Mathematical Issues Arising in the Geometric Complexity Theory Approach to $\mathbf{VP}\neq\mathbf{VNP}$

Peter Bürgisser, J. M. Landsberg, Laurent Manivel, Jerzy Weyman
2011 SIAM journal on computing (Print)  
We discuss the geometry of orbit closures and the asymptotic behavior of Kronecker coefficients in the context of the geometric complexity theory program to prove a variant of Valiant's algebraic analogue  ...  We also describe the precise separation of complexity classes that their program proposes to demonstrate.  ...  This paper is an outgrowth of the AIM workshop Geometry and representation theory of tensors for computer science, statistics and other areas, July 21-25, 2008, and the authors gratefully thank AIM and  ... 
doi:10.1137/090765328 fatcat:mf7w367eqreopbr76y5v6ihtaq

P versus NP and geometry [article]

J.M. Landsberg
2010 arXiv   pre-print
NP, present several results that illustrate the role of group actions in complexity theory, and make a first step towards completely geometric definitions of complexity classes.  ...  I describe three geometric approaches to resolving variants of P v.  ...  VNP is Valiant's algebraic analogue of NP, see §6 for a definition.  ... 
arXiv:0910.2443v2 fatcat:aml4xmebqjfrxonz5bcwusafpa

Progress in Computational Complexity Theory

Jin-Yi Cai, Hong Zhu
2005 Journal of Computer Science and Technology  
connectivity problem; deterministic polynomial-time primality test; lattice complexity, worst-case to averagecase reductions; pseudorandomness and extractor constructions; and Valiant's new theory of  ...  We will discuss the PCP Theorem, its implications to inapproximability on combinatorial optimization problems; space bounded computations, especially deterministic logspace algorithm for undirected graph  ...  We also thank Vinay Choudhary, Rakesh Kumar and Anand Sinha for many interesting discussions, and to Vinay Choudhary for his help in the bibliography.  ... 
doi:10.1007/s11390-005-0735-4 fatcat:67sjhrf4djc3hkhmyla45r63n4

The Computational Complexity of Plethysm Coefficients

Nick Fischer, Christian Ikenmeyer
2020 Computational Complexity  
The role of the Kronecker coefficients in that setting is taken by the so-called plethysm coefficients: These are the multiplicities in the coordinate rings of spaces of polynomials.  ...  While tensors are an interesting test bed for GCT ideas, the far-away goal is the separation of algebraic complexity classes.  ...  The author cc The Complexity of Plethysm Coefficients Page 37 of 43 8  ... 
doi:10.1007/s00037-020-00198-4 fatcat:kl75seyn2vfatj7eqyfhio6w4y

Deterministic Black-Box Identity Testing $pi$-Ordered Algebraic Branching Programs

Maurice Jansen, Youming Qiao, Jayalal Sarma M.N., Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
Our next set of results investigates the computational limitations of OABPs. It is shown that any OABP computing the determinant or permanent requires size Ω(2 n /n) and read Ω(2 n /n 2 ).  ...  One can think of OABPs as being the arithmetic analogue of ordered binary decision diagrams (OBDDs). We say an ABP A is of read r, if any variable appears at most r times in A.  ...  classes VP and VNP are distinct.  ... 
doi:10.4230/lipics.fsttcs.2010.296 dblp:conf/fsttcs/JansenQS10 fatcat:bfez3ibuxrcrjbzj5fdicb4dqq

Linear Stochastic Systems: A White Noise Approach

Daniel Alpay, David Levanony
2009 Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications  
Kaashoek Vrije Universiteit, The Netherlands Simple examples, due to Gohberg and Heinig [1] , show that for regular matrix polynomials it can happen that the null space of the block matrix analogue of  ...  However, if D is not a vector space over C then κ D (A, λ) provides only incomplete information about the mobility of λ under small perturbations from D.  ... 
doi:10.1007/s10440-009-9461-1 fatcat:2sbydn4vobgsnfq7szugarnqpy

Circuit complexity, proof complexity, and polynomial identity testing [article]

Joshua A. Grochow, Toniann Pitassi
2014 arXiv   pre-print
than lower bounds on the corresponding circuit classes.  ...  the difficulty of lower bounds on AC^0[p]-Frege, or b) AC^0[p]-Frege cannot efficiently prove the depth d PIT axioms, and hence we have a lower bound on AC^0[p]-Frege.  ...  Acknowledgments We thank David Liu for many interesting discussions, and for collaborating with us on some of the open questions posed in this paper.  ... 
arXiv:1404.3820v1 fatcat:2nerc6uatvdh5pqwtrhelt6jvq

Circuit Complexity, Proof Complexity, and Polynomial Identity Testing

Joshua A. Grochow, Toniann Pitassi
2014 2014 IEEE 55th Annual Symposium on Foundations of Computer Science  
than lower bounds on the corresponding circuit classes.  ...  Circuit Complexity, Proof Complexity, and PIT -J. A. Grochow and T. Pitassi From the proof of this result, together with one of our simulation results (Proposition 2.2), we also get: Corollary 1.2.  ...  Acknowledgments We thank David Liu for many interesting discussions, and for collaborating with us on some of the open questions posed in this paper.  ... 
doi:10.1109/focs.2014.20 dblp:conf/focs/GrochowP14 fatcat:mhmjd72cr5gmfdgtfl4zgsfhsi

Geometric Complexity Theory: Introduction [article]

Ketan D. Mulmuley, Milind Sohoni
2007 arXiv   pre-print
Part I consists of the lecture notes for the course given by the first author in the spring quarter, 2007. It gives introduction to the basic structure of GCT.  ...  These lecture notes in conjunction with the article GCTflip1, which describes in detail the basic plan of GCT based on the principle called the flip, should provide a high level picture of GCT assuming  ...  Let C class (G) be the space of class functions on (G), and let (α, β) = 1 |G| g α(g)β(g) be the Hermitian form on C class Lemma 3.7.  ... 
arXiv:0709.0746v1 fatcat:dm4qzrceqzhwvpfbzh2a4izi24

Recent progress on scaling algorithms and applications [article]

Ankit Garg, Rafael Oliveira
2018 arXiv   pre-print
This survey is intended for a general computer science audience, and the only background required is basic knowledge of calculus and linear algebra, thereby making it accessible to graduate students and  ...  Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering.  ...  Acknowledgements We thank Vikraman Arvind for inviting us to write this survey for the EATCS complexity column (June 2018 issue) and Avi Wigderson for providing helpful comments on an earlier version of  ... 
arXiv:1808.09669v1 fatcat:eohzepzccfhandivheqyvslej4

On Agnostic Learning of Parities, Monomials, and Halfspaces

Vitaly Feldman, Parikshit Gopalan, Subhash Khot, Ashok Kumar Ponnuswami
2009 SIAM journal on computing (Print)  
We study the learnability of several fundamental concept classes in the agnostic learning framework of Haussler [Hau92] and Kearns et al. [KSS94].  ...  We use similar techniques to reduce learning of two other fundamental concept classes under the uniform distribution to learning of noisy parities.  ...  We would also like to thank Shaili Jain and the anonymous referees of CCC '06 and FOCS '06 for numerous helpful remarks, one of which simplified the proof of Theorem 8.  ... 
doi:10.1137/070684914 fatcat:on6brq4wyfchrl55fsdbhtevuq

Interactions of Computational Complexity Theory and Mathematics [article]

Avi Wigderson
2017 arXiv   pre-print
In my view, the breadth, depth, beauty and novelty of these connections is inspiring, and speaks to a great potential of future interactions (which indeed, are quickly expanding). We aim for variety.  ...  We give short, simple descriptions (without proofs or much technical detail) of ideas, motivations, results and connections; this will hopefully entice the reader to dig deeper.  ...  p ∈ F[X] G there is a t-variate polynomial r over F so that p = r(q 1 , q 2 , . . . , qt). 24 E.g. have small arithmetic circuits or formulae. space 25 .  ... 
arXiv:1710.09780v1 fatcat:js6k4t7gefcutfus6te4vxx6ty

Sentiment Analysis [chapter]

2017 Encyclopedia of Machine Learning and Data Mining  
Theor Comput Sci 261(1):119-156 Gold EM (1967) Language identification in the limit. Inf Control 10(5):447-474 Haussler D (1987) Bias, version spaces and Valiant's learning framework.  ...  That is, S F .n/ D sup x2X n jF x j: The shattering coefficient of a hypothesis class H is used in generalization bounds as an analogue to the class's size in the finite case.  ...  Letting each ' i and j denote generic first-order formula, we can perform the "cross-sum"˚of case statements in the following manner: Likewise, we can perform « ,˝, and max operations by respectively subtracting  ... 
doi:10.1007/978-1-4899-7687-1_100512 fatcat:ce4yyqo2czftzcx2kbauglh3fu

Spike-Timing-Dependent Plasticity [chapter]

2017 Encyclopedia of Machine Learning and Data Mining  
Theor Comput Sci 261(1):119-156 Gold EM (1967) Language identification in the limit. Inf Control 10(5):447-474 Haussler D (1987) Bias, version spaces and Valiant's learning framework.  ...  That is, S F .n/ D sup x2X n jF x j: The shattering coefficient of a hypothesis class H is used in generalization bounds as an analogue to the class's size in the finite case.  ...  Letting each ' i and j denote generic first-order formula, we can perform the "cross-sum"˚of case statements in the following manner: Likewise, we can perform « ,˝, and max operations by respectively subtracting  ... 
doi:10.1007/978-1-4899-7687-1_774 fatcat:2jprihjaxfbtpb3ttwuuz3u34y
« Previous Showing results 1 — 15 out of 24 results