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Identity Testing for Constant-Width, and Commutative, Read-Once Oblivious ABPs

Rohit Gurjar, Arpita Korwar, Nitin Saxena
unpublished
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 variable order.  ...  In particular, this gives the first polynomial time hitting-set for constant-width ROABP (known-order).  ...  Identity Testing for Constant-Width, and Commutative, Read-Once Oblivious ABPs 29:6  ... 
fatcat:ttmlf3rnp5he3pwjyboxn2xyvy

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.  ...  Impagliazzo-Nisan-Wigderson for read-once oblivious boolean branching programs.  ...  Hitting Set for Read-Once Oblivious ABPs In this section, we construct a hitting set for read-once oblivious ABPs.  ... 
arXiv:1209.2408v2 fatcat:piahhxizsjh3dcbpkx6fqztpdq

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).  ...  We also show that several other circuit classes can be black-box reduced to read-once oblivious ABPs, including set-multilinear ABPs (a generalization of depth 3 set-multilinear formulas), non-commutative  ...  Hitting Set for Read-Once Oblivious ABPs In this section, we construct a hitting set for read-once oblivious ABPs.  ... 
doi:10.1109/focs.2013.34 dblp:conf/focs/ForbesS13 fatcat:m6tsod2pnjcatlahg5zzke2b4a

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  
Given a permutation π of the n variables, for a π-ordered ABP (π-OABP), for any directed path p from s to t, a variable can appear at most once on p, and the order in which variables appear on p must respect  ...  We prove a strict separation for the computational power of read (r − 1) and read r OABPs.  ...  Identity testing OABPs reduces to PIT for non-commutative ABPs, and hence can be done non-black-box in polynomial time.  ... 
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

Matthew Anderson, Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka, Ben Lee Volk
2018 ACM Transactions on Computation Theory  
Another line of work focused on read-once oblivious ABPs (ROABPs, and we again refer to Section 1.1 for the exact definition).  ...  identity tests for this model [61] .  ...  Testing and Lower Bounds for Read-k Oblivious ABPs Lemma 2.5.  ... 
doi:10.1145/3170709 fatcat:fnoqrflnq5dzlgyvcpavkq3en4

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
We also study the polynomial identity testing (PIT) problem for this model and obtain a white-box subexponential-time PIT algorithm.  ...  Read-k oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ROABPs).  ...  Identity testing for read-k oblivious ABPs In this section we give our white-box identity testing algorithm for 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
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.  ...  Given a permutation π of n variables, for a π-ordered ABP (π-OABP), for any directed path p from source to sink, a variable can appear at most once on p, and the order in which variables appear on p must  ...  In [9] a polynomial-time non-black-box algorithm was given for identity testing non-commutative formulas, and more generally non-commutative ABPs.  ... 
arXiv:1002.1496v1 fatcat:ajcfflrs2vfqxdiu54jsyifrou

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.  ...  In particular, this gives the first polynomial-size hitting set for constant-width ROABP (known-order).  ...  In particular, it is a big open question to find an O(log n)-seed-length PRG for constant-width ROBPs (analogous to Corollary 3.7).  ... 
arXiv:1601.08031v1 fatcat:2m2louqen5effno2o6knvhvv7q

Quasipolynomial Hitting Sets for Circuits with Restricted Parse Trees

Ramprasad Saptharishi, Anamay Tengse, Michael Wagner
2018 Foundations of Software Technology and Theoretical Computer Science  
The above three results are extensions of the results of [2], [10] and [9] to the setting of UPT circuits, and hence also generalize their results in the commutative world from read-once oblivious algebraic  ...  bounded by a constant.  ...  We thank Nutan Limaye and Srikanth Srinivasan for numerous discussions that eventually led to these results.  ... 
doi:10.4230/lipics.fsttcs.2018.6 dblp:conf/fsttcs/SaptharishiT18 fatcat:lad7cqooujegtg7lkyobavnhyu

Pseudorandomness for Multilinear Read-Once Algebraic Branching Programs, in any Order [article]

Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka
2013 arXiv   pre-print
We give deterministic black-box polynomial identity testing algorithms for multilinear read-once oblivious algebraic branching programs (ROABPs), in n^(lg^2 n) time.  ...  Furthermore, our result has no known analogue in the model of read-once oblivious boolean branching programs with unknown order, as despite recent work there is no known pseudorandom generator for this  ...  The first two authors would like to thank Chandan Saha for explaining the work of Agrawal-Saha-Saxena [ASS12] to them.  ... 
arXiv:1309.5668v1 fatcat:jbjxqwhlujhjtlzpn55zntbuni

Hitting sets for multilinear read-once algebraic branching programs, in any order

Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka
2014 Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14  
We give deterministic black-box polynomial identity testing algorithms for multilinear read-once oblivious algebraic branching programs (ROABPs), in n O(lg 2 n) time. 1 Further, our algorithm is oblivious  ...  Furthermore, our result has no known analogue in the model of read-once oblivious boolean branching programs with unknown order, as despite recent work (eg.  ...  The first two authors would like to thank Chandan Saha for explaining the work of Agrawal-Saha-Saxena [ASS12] to them.  ... 
doi:10.1145/2591796.2591816 dblp:conf/stoc/ForbesSS14 fatcat:ipjeduquyvhc3ndiistq2qt6se

Explicit Noether Normalization for Simultaneous Conjugation via Polynomial Identity Testing [article]

Michael A. Forbes, Amir Shpilka
2013 arXiv   pre-print
algorithms for polynomial identity testing (PIT).  ...  We then observe that the weaker conjecture has recently been nearly settled by the authors, who gave quasipolynomial size hitting sets for the class of read-once oblivious algebraic branching programs  ...  The authors are grateful to Josh Grochow [Gro13] for bringing the works of Chistov-Ivanyos-Karpinski [CIK97] , Sergeichuk [Ser00] and Belitskiȋ [Bel83] to their attention, and for explaining these  ... 
arXiv:1303.0084v2 fatcat:mvpzlhkjnnelri4s6nezomojoe

Explicit Noether Normalization for Simultaneous Conjugation via Polynomial Identity Testing [chapter]

Michael A. Forbes, Amir Shpilka
2013 Lecture Notes in Computer Science  
black-box algorithms for polynomial identity testing (PIT).  ...  We then observe that the weaker conjecture has recently been nearly settled by the authors ([FS12]), who gave quasipolynomial size hitting sets for the class of read-once oblivious algebraic branching  ...  . • In a read-once oblivious ABP (ROABP) of (individual) degree < r, we have n := d, and for each edge e from V i−1 to V i , the weight is a univariate polynomial f e (x i ) ∈ F[x i ] of degree < r.  ... 
doi:10.1007/978-3-642-40328-6_37 fatcat:jd4yqz6a7jgdfewml4inacgsvm

Quasi-polynomial Hitting Sets for Circuits with Restricted Parse Trees [article]

Ramprasad Saptharishi, Anamay Tengse
2017 arXiv   pre-print
The above three results are extensions of the results of [AGKS15], [GKST15] and [GKS16] to the setting of UPT circuits, and hence also generalize their results in the commutative world from read-once oblivious  ...  of preimage-width is bounded by a constant.  ...  We thank Nutan Limaye and Srikanth Srinivasan for numerous discussions that eventually led to these results.  ... 
arXiv:1709.03068v2 fatcat:mqftewbdmfglxlddbiy7lx2sje

Black-box Identity Testing of Noncommutative Rational Formulas of Inversion Height Two in Deterministic Quasipolynomial-time [article]

V. Arvind and Abhranil Chatterjee and Partha Mukhopadhyay
2022 arXiv   pre-print
A central open problem in this area is to design efficient deterministic black-box identity testing algorithm for rational formulas.  ...  They introduced the Rational Identity Testing (RIT) problem which is to decide whether a noncommutative rational formula computes zero in the free skew field.  ...  We also consider commutative set-multilinear ABPs and read-once oblivious ABPs (ROABPs).  ... 
arXiv:2202.05693v1 fatcat:7tr6lmbrhfeaxc6y7r6j3xqgta
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