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Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs
[article]

2015
*
arXiv
*
pre-print

A

arXiv:1411.7341v2
fatcat:xq3h7gtmnvhmdelbttsq45kc5u
*read*-*once**oblivious**arithmetic**branching**program*(ROABP) is an*arithmetic**branching**program*(ABP) where each variable occurs in at most one layer. ... We give the first polynomial time whitebox*identity**test**for*a polynomial computed by a*sum**of*constantly many ROABPs. ... Part*of*the work was done during Dagstuhl Seminar 14391 on Algebra in Computational Complexity 2014. We thank anonymous referees*for*the useful suggestions. ...##
###
Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs

2016
*
Computational Complexity
*

A

doi:10.1007/s00037-016-0141-z
fatcat:wiaavkais5hkvdpu3l3hvqzovq
*read*-*once**oblivious**arithmetic**branching**program*(ROABP) is an*arithmetic**branching**program*(ABP) where each variable occurs in at most one layer. ... A*read*-*once**oblivious*ABP (ROABP) is an*arithmetic**branching**program*, where each variable occurs in at most one layer. ... Part*of*the work was done during Dagstuhl Seminar 14391 on Algebra in Computational Complexity 2014. We thank anonymous referees*for*the useful suggestions. ...##
###
Deterministic Identity Testing for Sum of Read-once Oblivious Arithmetic Branching Programs

2015
*
Computational Complexity Conference
*

A

doi:10.4230/lipics.ccc.2015.323
dblp:conf/coco/GurjarKST15
fatcat:joo2e6pbyjeznd2csdtrlq2lc4
*read*-*once**oblivious**arithmetic**branching**program*(ROABP) is an*arithmetic**branching**program*(ABP) where each variable occurs in at most one layer. ... A*read*-*once**oblivious*ABP (ROABP) is an*arithmetic**branching**program*, where each variable occurs in at most one layer. ... Part*of*the work was done during Dagstuhl Seminar 14391 on Algebra in Computational Complexity 2014. We thank anonymous referees*for*the useful suggestions. ...##
###
Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs

2018
*
ACM Transactions on Computation Theory
*

*Read*-k

*oblivious*algebraic

*branching*

*programs*are a natural generalization

*of*the well-studied model

*of*

*read*-

*once*

*oblivious*algebraic

*branching*

*program*(ROABPs). ...

*identity*

*tests*

*for*this model [61] . ... 30:12

*Identity*

*Testing*and Lower Bounds

*for*

*Read*-k

*Oblivious*ABPs Lemma 2.5. ...

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

2010
*
Foundations of Software Technology and Theoretical Computer Science
*

In this paper we study algebraic

doi:10.4230/lipics.fsttcs.2010.296
dblp:conf/fsttcs/JansenQS10
fatcat:bfez3ibuxrcrjbzj5fdicb4dqq
*branching**programs*(ABPs) with restrictions on the order and the number*of**reads**of*variables in the*program*. ... Our main result pertains to the polynomial*identity**testing*problem, i.e. the problem*of*deciding whether a given n-variate polynomial is*identical*to the zero polynomial or not. ... Black-box*Identity**testing**sum*-*of*-k ROFs was studied in [19] , and this was subsequently generalized to the*sum*-*of*-k*read*-*once*ABPs in [10] . ...##
###
Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs
[article]

2015
*
arXiv
*
pre-print

*Read*-k

*oblivious*algebraic

*branching*

*programs*are a natural generalization

*of*the well-studied model

*of*

*read*-

*once*

*oblivious*algebraic

*branching*

*program*(ROABPs). ... We also study the polynomial

*identity*

*testing*(PIT) problem

*for*this model and obtain a white-box subexponential-time PIT algorithm. ...

*Identity*

*tests*

*for*

*read*-k

*oblivious*ABPs

*Identity*

*tests*

*for*k-pass ABPs In this section we give PIT algorithms

*for*the class

*of*

*read*-k

*oblivious*ABPs. ...

##
###
Deterministic Black-Box Identity Testing π-Ordered Algebraic Branching Programs
[article]

2010
*
arXiv
*
pre-print

In this paper we study algebraic

arXiv:1002.1496v1
fatcat:ajcfflrs2vfqxdiu54jsyifrou
*branching**programs*(ABPs) with restrictions on the order and the number*of**reads**of*variables in the*program*. ... An ABP A is said to be*of**read*r, if any variable appears at most r times in A. Our main result pertains to the*identity**testing*problem. ... Black-box*Identity**testing**sum*-*of*-k ROFs was studied in [10] , and this was subsequently generalized to the*sum*-*of*-k*read*-*once*ABPs in [11] . ...##
###
Quasipolynomial-time Identity Testing of Non-Commutative and Read-Once Oblivious Algebraic Branching Programs
[article]

2013
*
arXiv
*
pre-print

We study the problem

arXiv:1209.2408v2
fatcat:piahhxizsjh3dcbpkx6fqztpdq
*of*obtaining*deterministic*black-box polynomial*identity**testing*algorithms (PIT)*for*algebraic*branching**programs*(ABPs) that are*read*-*once*and*oblivious*. ... and Impagliazzo-Nisan-Wigderson*for**read*-*once**oblivious*boolean*branching**programs*. ... Essentially, all these models can be cast as a problem*of*obtaining black-box PIT*for**read*-*once**oblivious**branching**programs*where each variable appears on a small number*of*edges. ...##
###
Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication
[chapter]

2000
*
Lecture Notes in Computer Science
*

*For*that reason two restricted models

*of*nondeterministic

*read*-

*once*

*branching*

*programs*are defined and a lower bound method is presented. ...

*Branching*

*programs*are a well established computation model

*for*Boolean functions, especially

*read*-

*once*

*branching*

*programs*have been studied intensively. ... Thanks to Detlef Sieling and Ingo Wegener

*for*fruitful discussions and to Stefan Droste

*for*proofreading. I also would like to thank the anonymous referees

*for*their helpful comments. ...

##
###
Quasipolynomial-Time Identity Testing of Non-commutative and Read-Once Oblivious Algebraic Branching Programs

2013
*
2013 IEEE 54th Annual Symposium on Foundations of Computer Science
*

We study the problem

doi:10.1109/focs.2013.34
dblp:conf/focs/ForbesS13
fatcat:m6tsod2pnjcatlahg5zzke2b4a
*of*obtaining efficient,*deterministic*, black-box polynomial*identity**testing*algorithms (PIT)*for**read*-*once**oblivious*algebraic*branching**programs*(ABPs). ... The main result in this paper is a quasi-polynomial time PIT algorithm in the black-box model*for**read*-*once**oblivious*algebraic*branching**programs*. ... Essentially, all these models can be cast as a problem*of*obtaining black-box PIT*for**read*-*once**oblivious**branching**programs*where each variable appears on a small number*of*edges. ...##
###
Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication

2001
*
RAIRO - Theoretical Informatics and Applications
*

*For*that reason two restricted models

*of*nondeterministic

*read*-

*once*

*branching*

*programs*are defined and a lower bound method is presented. ...

*Branching*

*programs*are a well established computation model

*for*Boolean functions, especially

*read*-

*once*

*branching*

*programs*have been studied intensively. ... Acknowledgement Thanks to Ingo Wegener

*for*several valuable hints and fruitful discussions and to Stefan Droste

*for*proofreading. ...

##
###
Pseudorandomness for Linear Length Branching Programs and Stack Machines
[chapter]

2012
*
Lecture Notes in Computer Science
*

We show the existence

doi:10.1007/978-3-642-32512-0_38
fatcat:ocakekaemvbqxcjkwpyrmgt7tm
*of*an explicit pseudorandom generator G*of*linear stretch such that*for*every constant k, the output*of*G is pseudorandom against: -*Oblivious**branching**programs*over alphabet {0, ...*For*the last result, we give a length-efficient simulation*of*such stack machines by non-*deterministic**branching**programs*(over large alphabet) whose accepting computations have a unique witness. ... Acknowledgements We are grateful to the anonymous referee that pointed out a significant flaw in the proof*of*a previous version*of*our main theorem. ...##
###
A Constant-Space Sequential Model of Computation for First-Order Logic

1998
*
Information and Computation
*

We define and justify a natural sequential model

doi:10.1006/inco.1998.2702
fatcat:whcebmo7yjek3mshmpo3w723he
*of*computation with a constant amount*of**read*write work space, despite unlimited (polynomial) access to*read*-only input and write-only output. ... The model is*deterministic*, uniform, and sequential. ... ACKNOWLEDGEMENTS I am grateful*for*discussions with Dave Mix Barrington and Sorin Istrail, who introduced me to the equivalence between constant-depth circuits and*read*-*once*constant-width*branching**programs*...##
###
A Guide to Learning Arithmetic Circuits

2016
*
Annual Conference Computational Learning Theory
*

In this paper, we exhibit several connections between learning algorithms

dblp:conf/colt/Volkovich16
fatcat:33mwk4ta4rbj5pngellfkjwjdu
*for**arithmetic*circuits and other problems. ... and equivalence queries iff they can be learned efficiently with membership queries only. • Low-query learning algorithms*for*certain classes*of*circuits imply explicit rigid matrices. • Learning algorithms ... Finally, the author would like to thank the anonymous referees*for*useful comments that improved the presentation*of*the paper. ...##
###
Identity Testing for Constant-Width, and Any-Order, Read-Once Oblivious Arithmetic Branching Programs
[article]

2016
*
arXiv
*
pre-print

We give improved hitting sets

arXiv:1601.08031v1
fatcat:2m2louqen5effno2o6knvhvv7q
*for*two special cases*of**Read*-*once**Oblivious**Arithmetic**Branching**Programs*(ROABP). First is the case*of*an ROABP with known order*of*the variables. ... The best previously known hitting set*for*this case had size (nw)^O( n) where n is the number*of*variables and w is the width*of*the ROABP. ... We conjecture a polynomial-time hitting-set*for*the unknown-order case in Conjecture 3.8. As mentioned earlier, the ideas here can help in finding a better PRG*for*ROBPs. ...
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