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

Rohit Gurjar and Arpita Korwar and Nitin Saxena and Thomas Thierauf
2015 arXiv   pre-print
A 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.  ... 
arXiv:1411.7341v2 fatcat:xq3h7gtmnvhmdelbttsq45kc5u

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

Rohit Gurjar, Arpita Korwar, Nitin Saxena, Thomas Thierauf
2016 Computational Complexity  
A 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.  ... 
doi:10.1007/s00037-016-0141-z fatcat:wiaavkais5hkvdpu3l3hvqzovq

Deterministic Identity Testing for Sum of Read-once Oblivious Arithmetic Branching Programs

Rohit Gurjar, Arpita Korwar, Nitin Saxena, Thomas Thierauf, Marc Herbstritt
2015 Computational Complexity Conference  
A 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.  ... 
doi:10.4230/lipics.ccc.2015.323 dblp:conf/coco/GurjarKST15 fatcat:joo2e6pbyjeznd2csdtrlq2lc4

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  
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.  ... 
doi:10.1145/3170709 fatcat:fnoqrflnq5dzlgyvcpavkq3en4

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  
In this paper we study algebraic 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] .  ... 
doi:10.4230/lipics.fsttcs.2010.296 dblp:conf/fsttcs/JansenQS10 fatcat:bfez3ibuxrcrjbzj5fdicb4dqq

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

Matthew Anderson, Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka, Ben Lee Volk
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.  ... 
arXiv:1511.07136v1 fatcat:ndotfilu25h2zji75r4iajbkmq

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

Maurice Jansen and Youming Qiao and Jayalal Sarma
2010 arXiv   pre-print
In this paper we study algebraic 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] .  ... 
arXiv:1002.1496v1 fatcat:ajcfflrs2vfqxdiu54jsyifrou

Quasipolynomial-time Identity Testing of Non-Commutative and Read-Once Oblivious Algebraic Branching Programs [article]

Michael A. Forbes, Amir Shpilka
2013 arXiv   pre-print
We study the problem 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.  ... 
arXiv:1209.2408v2 fatcat:piahhxizsjh3dcbpkx6fqztpdq

Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication [chapter]

Beate Bollig
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.  ... 
doi:10.1007/3-540-44612-5_18 fatcat:zak2tm34vnhadf5igohiptdlue

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

Michael A. Forbes, Amir Shpilka
2013 2013 IEEE 54th Annual Symposium on Foundations of Computer Science  
We study the problem 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.  ... 
doi:10.1109/focs.2013.34 dblp:conf/focs/ForbesS13 fatcat:m6tsod2pnjcatlahg5zzke2b4a

Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication

Beate Bollig
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.  ... 
doi:10.1051/ita:2001113 fatcat:yjaouw2vpjboznwowlup3xyb3e

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

Andrej Bogdanov, Periklis A. Papakonstantinou, Andrew Wan
2012 Lecture Notes in Computer Science  
We show the existence 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.  ... 
doi:10.1007/978-3-642-32512-0_38 fatcat:ocakekaemvbqxcjkwpyrmgt7tm

A Constant-Space Sequential Model of Computation for First-Order Logic

Steven Lindell
1998 Information and Computation  
We define and justify a natural sequential model 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  ... 
doi:10.1006/inco.1998.2702 fatcat:whcebmo7yjek3mshmpo3w723he

A Guide to Learning Arithmetic Circuits

Ilya Volkovich
2016 Annual Conference Computational Learning Theory  
In this paper, we exhibit several connections between learning algorithms 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.  ... 
dblp:conf/colt/Volkovich16 fatcat:33mwk4ta4rbj5pngellfkjwjdu

Identity Testing for Constant-Width, and Any-Order, Read-Once Oblivious Arithmetic Branching Programs [article]

Rohit Gurjar and Arpita Korwar and Nitin Saxena
2016 arXiv   pre-print
We give improved hitting sets 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.  ... 
arXiv:1601.08031v1 fatcat:2m2louqen5effno2o6knvhvv7q
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