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`

.

## Filters

##
###
A syntactical analysis of non-size-increasing polynomial time computation
[article]

2001
*
arXiv
*
pre-print

*A*

*syntactical*proof is given that all functions definable in

*a*certain affine linear typed lambda-calculus with iteration in all types are

*polynomial*

*time*

*computable*. ... The proof provides explicit

*polynomial*bounds that can easily be calculated. ... Full

*Polynomial*

*Time*The system so far only contains

*non*-

*size*-

*increasing*functions, and hence cannot contain all Ptime functions. ...

##
###
A syntactical analysis of non-size-increasing polynomial time computation

2002
*
ACM Transactions on Computational Logic
*

*A*

*syntactical*proof is given that all functions definable in

*a*certain affine linear typed λ-calculus with iteration in all types are

*polynomial*

*time*

*computable*. ... The proof provides explicit

*polynomial*bounds that can easily be calculated. ... On this type, we can then define functions that are semantically

*size*-

*increasing*, like the extension

*of*

*a*Turing tape, but are from

*a*

*syntactic*point

*of*view

*non*-

*size*-

*increasing*, in that they do not require ...

##
###
A syntactical analysis of non-size-increasing polynomial time computation

*
Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
*

*A*

*syntactical*proof is given that all functions definable in

*a*certain affine linear typed λ-calculus with iteration in all types are

*polynomial*

*time*

*computable*. ... The proof provides explicit

*polynomial*bounds that can easily be calculated. ... On this type, we can then define functions that are semantically

*size*-

*increasing*, like the extension

*of*

*a*Turing tape, but are from

*a*

*syntactic*point

*of*view

*non*-

*size*-

*increasing*, in that they do not require ...

##
###
Tensor-rank and lower bounds for arithmetic formulas

2010
*
Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10
*

We show that for any n-variate set-multilinear

doi:10.1145/1806689.1806780
dblp:conf/stoc/Raz10
fatcat:w7gp4d3obzbz7iblbub73676se
*polynomial*f*of*degree r, if there exists*a*(fanin-2) formula*of**size*s and depth d for f then there exists*a*set-multilinear formula*of**size*O ((d + 2) r ...*of*degree r, if there exists*a*(fanin-2) formula*of**size*s and depth d for f then there exists*a*homogeneous formula*of**size*O d+r+1 r · s for f . ... Therefore, weight(u) = 1, since*a*higher weight*increases*the*size**of*the extended-formula without*increasing*its*syntactic*-rank. Let u be*a**non*-leaf node with children u 1 , u 2 . ...##
###
Tensor-Rank and Lower Bounds for Arithmetic Formulas

2013
*
Journal of the ACM
*

We show that for any n-variate set-multilinear

doi:10.1145/2535928
fatcat:eozbyhiosrbsvohbpiih4tk3eq
*polynomial*f*of*degree r, if there exists*a*(fanin-2) formula*of**size*s and depth d for f then there exists*a*set-multilinear formula*of**size*O ((d + 2) r ...*of*degree r, if there exists*a*(fanin-2) formula*of**size*s and depth d for f then there exists*a*homogeneous formula*of**size*O d+r+1 r · s for f . ... Therefore, weight(u) = 1, since*a*higher weight*increases*the*size**of*the extended-formula without*increasing*its*syntactic*-rank. Let u be*a**non*-leaf node with children u 1 , u 2 . ...##
###
Resource Trade-offs in Syntactically Multilinear Arithmetic Circuits

2013
*
Computational Complexity
*

The class

doi:10.1007/s00037-013-0072-x
fatcat:6jg6o6x5k5bkvm6tazo5dtm4fe
*of**polynomials**computable*by*polynomial**size*log depth arithmetic circuits (VNC 1 ) is known to be*computable*by constant width*polynomial*degree circuits (VsSC 0 ), but whether the converse ... Along the way we also observe*a*characterisation*of*the class NC 1 in terms*of**a*restricted class*of*planar branching programs*of**polynomial**size*. ... We thank the anonymous referees*of*MFCS 2008, CSR 2009, and*of*this journal for their insightful comments and suggestions for improving the presentation*of*the paper. ...##
###
Tensor Reconstruction Beyond Constant Rank
[article]

2022
*
arXiv
*
pre-print

*A*deterministic algorithm that reconstructs

*polynomials*

*computed*by Σ^[k]⋀^[d]Σ circuits in

*time*𝗉𝗈𝗅𝗒(n,d,c) ·𝗉𝗈𝗅𝗒(k)^k^k^10 2. ...

*A*randomized algorithm that reconstructs

*polynomials*

*computed*by multilinear Σ^k]∏^[d]Σ circuits in

*time*𝗉𝗈𝗅𝗒(n,d,c) · k^k^k^k^O(k) 3. ... , we know that the restricted

*polynomial*has

*a*small set-multilinear circuit, and thus the algorithm can find it). ...

##
###
GUBS Upper Bound Solver (Extended Abstract)

2017
*
Electronic Proceedings in Theoretical Computer Science
*

GUBS now forms the backbone

doi:10.4204/eptcs.248.6
fatcat:jfdsl4gdqnbcvg64oboggem5wq
*of*HoSA,*a*tool for analysing space and*time*complexity*of*higher-order functional programs automatically. ... GUBS is*a*dedicated constraint solver over the naturals for inequalities formed over uninterpreted function symbols and standard arithmetic operations. ... The considered examples are the constraints generated from HoSA for the*time*and*size*complexity*analysis**of**a*set*of*functional programs. ...##
###
Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs

2018
*
ACM Transactions on Computation Theory
*

In this work, we give an exponential lower bound

doi:10.1145/3170709
fatcat:fnoqrflnq5dzlgyvcpavkq3en4
*of*exp(n/k O(k) ) on the width*of*any read-k oblivious ABP*computing*some explicit multilinear*polynomial*f that is*computed*by*a**polynomial**size*depth- ... We also study the*polynomial*identity testing (PIT) problem for this model and obtain*a*white-box subexponential-*time*PIT algorithm. ... by*a*linear-*size**syntactic*read-(k + 1)-*times*branching program such that every*syntactic*read-k-*times*branching program*computing*f must have*size*exp(Ω(n 1/k /2 O(k) )). ...##
###
On the Expressive Efficiency of Sum Product Networks
[article]

2015
*
arXiv
*
pre-print

as

arXiv:1411.7717v3
fatcat:kacqxdktsjdatdnalcpsfhsxdm
*a*function*of*their*size*and depth. ... Sum Product Networks (SPNs) are*a*recently developed class*of*deep generative models which*compute*their associated unnormalized density functions using*a*special type*of*arithmetic circuit. ... James Martens was supported by*a*Google Fellowship. ...##
###
Objects in Polynomial Time
[chapter]

2015
*
Lecture Notes in Computer Science
*

*A*type system based on

*non*-interference and data ramification principles is introduced in order to capture the set

*of*functions

*computable*in

*polynomial*

*time*on OO programs. ... The studied language is general enough to capture most OO constructs and our characterization is quite expressive as it allows the

*analysis*

*of*

*a*combination

*of*imperative loops and

*of*data ramification ... Characterization

*of*

*polynomial*

*time*In this section, we show the main result

*of*our paper:

*a*characterization

*of*the class

*of*functions

*computable*in

*polynomial*

*time*by

*a*Turing Machine, known as F P

*time*...

##
###
Application of formal languages in polynomial transformations of instances between NP-complete problems

2013
*
Journal of Zhejiang University SCIENCE C
*

The proposed approach, which consists

doi:10.1631/jzus.c1200349
fatcat:3oemuj5bunfqtduzuhnz5czsru
*of*using formal language theory for*polynomial*transformations, is more robust, more practical, and faster to apply to real problems than the theory*of**polynomial*... We propose the usage*of*formal languages for expressing instances*of*NP-complete problems for their application in*polynomial*transformations. ...*time*by*a**non*-deterministic one-tape Turing machine. ...##
###
Balancing Bounded Treewidth Circuits
[chapter]

2010
*
Lecture Notes in Computer Science
*

From this we derive the analogous statement for

doi:10.1007/978-3-642-13182-0_21
fatcat:zbid7xnlpzaerac2zromqibccq
*syntactically*multilinear arithmetic circuits, which strengthens*a*theorem*of*Mahajan and Rao. ... For both arithmetic and Boolean circuits, it is shown that any circuit*of**size*n^O(1) and treewidth O(^i n) can be simulated by*a*circuit*of*width O(^i+1 n) and*size*n^c, where c = O(1), if i=0, and c= ...*A*straigtforward*analysis*gives that this*computation*takes*time**polynomial*in the length*of*the input. ...##
###
Page 3764 of Mathematical Reviews Vol. , Issue 2003e
[page]

2003
*
Mathematical Reviews
*

{For the entire collection see MR 2003a:68014. }
2003e:68032 68Q15 03B40 03B47 03D15 68N18 Aehlig, Klaus (D-MNCH-MI; Munich); Schwichtenberg, Helmut (D-MNCH-MI; Munich)

*A**syntactical**analysis**of**non*-*size*-*increasing*...*polynomial**time**computation*. ...##
###
The Combinatorics of Non-determinism

2013
*
Foundations of Software Technology and Theoretical Computer Science
*

Following the symbolic method

doi:10.4230/lipics.fsttcs.2013.425
dblp:conf/fsttcs/BodiniGP13
fatcat:vnfiwh46nzb43pm3264uano4tq
*of*analytic combinatorics, we study the*size**of*the*computation*trees induced by typical*non*-deterministic processes, providing*a*precise quantitative measure*of*the so-called ... In this paper we further explore this connection by studying the rich combinatorics*of*partially*increasing*structures underlying the operator*of**non*-deterministic choice. ... The global choice is obtained from Algorithm 1 in*time*linear in the*size**of*the*polynomial*P(x) (represented as*a*DAG) because each coefficient contains at most one occurrence*of**a*parameter y v . ...
« Previous

*Showing results 1 — 15 out of 9,520 results*