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

unpublished

We give improved hitting-sets

fatcat:ttmlf3rnp5he3pwjyboxn2xyvy
*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 ...##
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Quasipolynomial-time Identity Testing of Non-Commutative and Read-Once Oblivious Algebraic Branching Programs
[article]

2013
*
arXiv
*
pre-print

We study the problem of obtaining deterministic black-box polynomial

arXiv:1209.2408v2
fatcat:piahhxizsjh3dcbpkx6fqztpdq
*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*. ...##
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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 of obtaining efficient, deterministic, black-box polynomial

doi:10.1109/focs.2013.34
dblp:conf/focs/ForbesS13
fatcat:m6tsod2pnjcatlahg5zzke2b4a
*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*. ...##
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Deterministic Black-Box Identity Testing $pi$-Ordered Algebraic Branching Programs

2010
*
Foundations of Software Technology and Theoretical Computer Science
*

Given a permutation π of the n variables,

doi:10.4230/lipics.fsttcs.2010.296
dblp:conf/fsttcs/JansenQS10
fatcat:bfez3ibuxrcrjbzj5fdicb4dqq
*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. ...##
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Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs

2018
*
ACM Transactions on Computation Theory
*

Another line of work focused on

doi:10.1145/3170709
fatcat:fnoqrflnq5dzlgyvcpavkq3en4
*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. ...##
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Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs
[article]

2015
*
arXiv
*
pre-print

We also study the polynomial

arXiv:1511.07136v1
fatcat:ndotfilu25h2zji75r4iajbkmq
*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*. ...##
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Deterministic Black-Box Identity Testing π-Ordered Algebraic Branching Programs
[article]

2010
*
arXiv
*
pre-print

An

arXiv:1002.1496v1
fatcat:ajcfflrs2vfqxdiu54jsyifrou
*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*. ...##
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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. ... 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). ...##
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Quasipolynomial Hitting Sets for Circuits with Restricted Parse Trees

2018
*
Foundations of Software Technology and Theoretical Computer Science
*

The above three results are extensions of the results of [2], [10]

doi:10.4230/lipics.fsttcs.2018.6
dblp:conf/fsttcs/SaptharishiT18
fatcat:lad7cqooujegtg7lkyobavnhyu
*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. ...##
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Pseudorandomness for Multilinear Read-Once Algebraic Branching Programs, in any Order
[article]

2013
*
arXiv
*
pre-print

We give deterministic black-box polynomial

arXiv:1309.5668v1
fatcat:jbjxqwhlujhjtlzpn55zntbuni
*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. ...##
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Hitting sets for multilinear read-once algebraic branching programs, in any order

2014
*
Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14
*

We give deterministic black-box polynomial

doi:10.1145/2591796.2591816
dblp:conf/stoc/ForbesSS14
fatcat:ipjeduquyvhc3ndiistq2qt6se
*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. ...##
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Explicit Noether Normalization for Simultaneous Conjugation via Polynomial Identity Testing
[article]

2013
*
arXiv
*
pre-print

algorithms

arXiv:1303.0084v2
fatcat:mvpzlhkjnnelri4s6nezomojoe
*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 ...##
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Explicit Noether Normalization for Simultaneous Conjugation via Polynomial Identity Testing
[chapter]

2013
*
Lecture Notes in Computer Science
*

black-box algorithms

doi:10.1007/978-3-642-40328-6_37
fatcat:jd4yqz6a7jgdfewml4inacgsvm
*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. ...##
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Quasi-polynomial Hitting Sets for Circuits with Restricted Parse Trees
[article]

2017
*
arXiv
*
pre-print

The above three results are extensions of the results of [AGKS15], [GKST15]

arXiv:1709.03068v2
fatcat:mqftewbdmfglxlddbiy7lx2sje
*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. ...##
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Black-box Identity Testing of Noncommutative Rational Formulas of Inversion Height Two in Deterministic Quasipolynomial-time
[article]

2022
*
arXiv
*
pre-print

A central open problem in this area is to design efficient deterministic black-box

arXiv:2202.05693v1
fatcat:7tr6lmbrhfeaxc6y7r6j3xqgta
*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). ...
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