Filters








9,493 Hits in 5.4 sec

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

Klaus Aehlig, Helmut Schwichtenberg
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.  ... 
arXiv:cs/0011037v2 fatcat:lbkjg5a3lfbahldc2zmzrdknei

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

Klaus Aehlig, Helmut Schwichtenberg
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  ... 
doi:10.1145/507382.507386 fatcat:pcrpkr7mine3lfljuxu7obqnsu

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

K. Aehlig, H. Schwichtenberg
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  ... 
doi:10.1109/lics.2000.855758 dblp:conf/lics/AehligS00 fatcat:3da5ldz6ofaklckxozjcs57pva

Tensor-rank and lower bounds for arithmetic formulas

Ran Raz
2010 Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10  
We show that for any n-variate set-multilinear 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 .  ... 
doi:10.1145/1806689.1806780 dblp:conf/stoc/Raz10 fatcat:w7gp4d3obzbz7iblbub73676se

Tensor-Rank and Lower Bounds for Arithmetic Formulas

Ran Raz
2013 Journal of the ACM  
We show that for any n-variate set-multilinear 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 .  ... 
doi:10.1145/2535928 fatcat:eozbyhiosrbsvohbpiih4tk3eq

Resource Trade-offs in Syntactically Multilinear Arithmetic Circuits

Maurice Jansen, Meena Mahajan, B. V. Raghavendra Rao
2013 Computational Complexity  
The class 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.  ... 
doi:10.1007/s00037-013-0072-x fatcat:6jg6o6x5k5bkvm6tazo5dtm4fe

Tensor Reconstruction Beyond Constant Rank [article]

Shir Peleg, Amir Shpilka, Ben Lee Volk
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).  ... 
arXiv:2209.04177v1 fatcat:7hyqmmah7rf6rnxhw5uj3zj3hy

GUBS Upper Bound Solver (Extended Abstract)

Martin Avanzini, Michael Schaper
2017 Electronic Proceedings in Theoretical Computer Science  
GUBS now forms the backbone 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.  ... 
doi:10.4204/eptcs.248.6 fatcat:jfdsl4gdqnbcvg64oboggem5wq

Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs

Matthew Anderson, Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka, Ben Lee Volk
2018 ACM Transactions on Computation Theory  
In this work, we give an exponential lower bound 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) )).  ... 
doi:10.1145/3170709 fatcat:fnoqrflnq5dzlgyvcpavkq3en4

On the Expressive Efficiency of Sum Product Networks [article]

James Martens, Venkatesh Medabalimi
2015 arXiv   pre-print
as 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.  ... 
arXiv:1411.7717v3 fatcat:kacqxdktsjdatdnalcpsfhsxdm

Objects in Polynomial Time [chapter]

Emmanuel Hainry, Romain Péchoux
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  ... 
doi:10.1007/978-3-319-26529-2_21 fatcat:rg76msfl4ncihclnvcnuip3zs4

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

Jorge A. Ruiz-Vanoye, Joaquín Pérez-Ortega, Rodolfo A. Pazos Rangel, Ocotlán Díaz-Parra, Héctor J. Fraire-Huacuja, Juan Frausto-Solís, Gerardo Reyes-Salgado, Laura Cruz-Reyes
2013 Journal of Zhejiang University SCIENCE C  
The proposed approach, which consists 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.  ... 
doi:10.1631/jzus.c1200349 fatcat:3oemuj5bunfqtduzuhnz5czsru

Balancing Bounded Treewidth Circuits [chapter]

Maurice Jansen, Jayalal Sarma M.N.
2010 Lecture Notes in Computer Science  
From this we derive the analogous statement for 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.  ... 
doi:10.1007/978-3-642-13182-0_21 fatcat:zbid7xnlpzaerac2zromqibccq

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

Olivier Bodini, Antoine Genitrini, Frédéric Peschanski, Marc Herbstritt
2013 Foundations of Software Technology and Theoretical Computer Science  
Following the symbolic method 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 .  ... 
doi:10.4230/lipics.fsttcs.2013.425 dblp:conf/fsttcs/BodiniGP13 fatcat:vnfiwh46nzb43pm3264uano4tq
« Previous Showing results 1 — 15 out of 9,493 results