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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

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

2018
*
ACM Transactions on Computation Theory
*

*identity*

*tests*

*for*this model [61] . ... Another line

*of*work focused on

*read*-

*once*oblivious

*ABPs*(ROABPs, and we again refer to Section 1.1

*for*the exact definition). ... 30:12

*Identity*

*Testing*and Lower Bounds

*for*

*Read*-k Oblivious

*ABPs*Lemma 2.5. ...

##
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Deterministic Identity Testing of Read-Once Algebraic Branching Programs
[article]

2009
*
arXiv
*
pre-print

In this paper we study polynomial

arXiv:0912.2565v1
fatcat:qn47ye5kdffdzf7rv6eizzlzie
*identity**testing**of**sums**of*k*read*-*once*algebraic branching programs (Σ_k-RO-*ABPs*), generalizing the work in (Shpilka and Volkovich 2008,2009), who considered*sums**of*... This implies we have a*deterministic*polynomial time algorithm*for**testing*whether the*sum**of*a constant number*of*RO-*ABPs*computes the zero polynomial. 2) Given black-box access to the RO-*ABPs*computing ... The results we will mention next make progress towards*identity**testing**read*-*once*determinantal expressions. ...##
###
Identity Testing, Multilinearity Testing, and Monomials in Read-Once/Twice Formulas and Branching Programs
[chapter]

2012
*
Lecture Notes in Computer Science
*

The simplest kind

doi:10.1007/978-3-642-32589-2_57
fatcat:3y5yafrv4bgvfjhmbqbkhnq3nu
*of*formulas are*read*-*once*formulas ROFs: every variable appears at most*once*.*Deterministic*polynomial-time algorithms*for*ACIT on such formulas are trivial. ...*Deterministic**identity**testing*algorithms are known*for*depth-2 crcuits,*for*depth-3 circuits with restrictions on the top fanin, and*for*restricted depth-4 circuits. ... We have shown that on*read*-*once*formulas and occur-*once*branching programs, the complexity*of*ZMC and ExistExtMon does reduce drastically. ...##
###
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 ... 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] . ...##
###
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**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*. ...##
###
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*). ... Indeed, the famous*deterministic*primality*testing*algorithm*of*Agrawal, Kayal and Saxena [AKS04] is based on derandomizing a specific polynomial*identity*. ... In [AMS10] , Arvind, Mukhopadhyay and Srinivasan gave a*deterministic*black-box algorithm*for**identity**testing**of*sparse non-commutative polynomials. ...##
###
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. ... This class has an*deterministic*white-box polynomial*identity**testing*algorithm (due to Raz and Shpilka), but prior to this work there was no known such black-box algorithm. ... In [AMS10] , Arvind, Mukhopadhyay and Srinivasan gave a*deterministic*black-box algorithm*for**identity**testing**of*sparse non-commutative polynomials. ...##
###
Equivalence Testing of Weighted Automata over Partially Commutative Monoids
[article]

2020
*
arXiv
*
pre-print

As a consequence, we also obtain the first

arXiv:2002.08633v2
fatcat:crtbwywtx5hvzjntd5nz25sliq
*deterministic*quasi-polynomial time algorithms*for*multiplicity equivalence*testing**of*k-tape automata and*for*equivalence*testing**of**deterministic*k-tape automata ... We obtain randomized polynomial-time algorithm*for*multiplicity equivalence*testing**of*automata over such monoids. ... In particular, we are grateful to an anonymous reviewer*for*suggesting simplified proofs*for*some lemmas, the concept*of*valid automata, and pointing out the earlier results related to partially commutative ...##
###
Monomials, multilinearity and identity testing in simple read-restricted circuits

2014
*
Theoretical Computer Science
*

We give a

doi:10.1016/j.tcs.2014.01.005
fatcat:3dljougmizacfgno3bu4l5qnmi
*deterministic*polynomial time algorithm*for*this problem when the inputs are*read*-twice or readthrice formulas. ... We study the problem*of**testing*if the polynomial computed by an arithmetic circuit is*identically*zero. ... MonCount is #P complete*for*the*sum**of*two monotone*read*-*once*formulas. Proof. First we show hardness. ...##
###
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

arXiv:2202.05693v1
fatcat:7tr6lmbrhfeaxc6y7r6j3xqgta
*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). ...##
###
Quasipolynomial Hitting Sets for Circuits with Restricted Parse Trees

2018
*
Foundations of Software Technology and Theoretical Computer Science
*

The above three results are extensions

doi:10.4230/lipics.fsttcs.2018.6
dblp:conf/fsttcs/SaptharishiT18
fatcat:lad7cqooujegtg7lkyobavnhyu
*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 ... size*for*FewPT circuits (circuits with constantly many parse tree shapes), An explicit hitting set*of*polynomial size*for*UPT circuits (*of*known parse tree shape), when a parameter*of*preimage-width is ... We thank Rohit Gurjar*for*pointing out a subtlety in a previous draft*of*this paper, and also thank Amir Shpilka*for*inviting RS to Tel Aviv University (where this discussion took place). ...##
###
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 ... , to polynomial*identity**testing**of**ABPs*. ...##
###
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 ... Acknowledgments The first author would like to thank Peter Bürgisser*for*explaining the work*of*Mulmuley, and the Complexity Theory week at Mathematisches Forschungsinstitut Oberwolfach*for*facilitating ...##
###
Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs

2016
*
Computational Complexity
*

circuits [22, 10, 4] ,

doi:10.1007/s00037-016-0141-z
fatcat:wiaavkais5hkvdpu3l3hvqzovq
*read*-*once*oblivious*ABP*(ROABP) [22, 12, 9, 3] . ... 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. ...
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