Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > KEYWORD > PIT:
Reports tagged with PIT:
TR07-042 | 7th May 2007
Zohar Karnin, Amir Shpilka

Black Box Polynomial Identity Testing of Depth-3 Arithmetic Circuits with Bounded Top Fan-in

Revisions: 2 , Comments: 1

In this paper we consider the problem of determining whether an
unknown arithmetic circuit, for which we have oracle access,
computes the identically zero polynomial. Our focus is on depth-3
circuits with a bounded top fan-in. We obtain the following
results.

1. A quasi-polynomial time deterministic black-box identity testing algorithm ... more >>>


TR13-011 | 10th January 2013
Nader Bshouty

Multilinear Complexity is Equivalent to Optimal Tester Size

In this paper we first show that Tester for an $F$-algebra $A$
and multilinear forms (see Testers and their Applications ECCC 2012) is equivalent to multilinear
algorithm for the product of elements in $A$
(see Algebraic
complexity theory. vol. 315, Springer-Verlag). Our
result is constructive in deterministic polynomial time. ... more >>>


TR13-174 | 6th December 2013
Manindra Agrawal, Rohit Gurjar, Arpita Korwar, Nitin Saxena

Hitting-sets for low-distance multilinear depth-$3$

The depth-$3$ model has recently gained much importance, as it has become a stepping-stone to understanding general arithmetic circuits. Its restriction to multilinearity has known exponential lower bounds but no nontrivial blackbox identity tests. In this paper we take a step towards designing such hitting-sets. We define a notion of ... more >>>


TR14-085 | 29th June 2014
Manindra Agrawal, Rohit Gurjar, Arpita Korwar, Nitin Saxena

Hitting-sets for ROABP and Sum of Set-Multilinear circuits

We give a $n^{O(\log n)}$-time ($n$ is the input size) blackbox polynomial identity testing algorithm for unknown-order read-once oblivious algebraic branching programs (ROABP). The best time-complexity known for this class was $n^{O(\log^2 n)}$ due to Forbes-Saptharishi-Shpilka (STOC 2014), and that too only for multilinear ROABP. We get rid of their ... more >>>


TR14-158 | 26th November 2014
Rohit Gurjar, Arpita Korwar, Nitin Saxena, Thomas Thierauf

Deterministic Identity Testing for Sum of Read Once ABPs

Revisions: 2

A read once ABP is an arithmetic branching program with each variable occurring 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. We also give a corresponding blackbox algorithm with quasi-polynomial time complexity, i.e. ... more >>>


TR16-009 | 28th January 2016
Rohit Gurjar, Arpita Korwar, Nitin Saxena

Identity Testing for constant-width, and commutative, read-once oblivious ABPs

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. The best hitting-set known for this case had cost $(nw)^{O(\log n)}$, where $n$ is the number of variables and $w$ is the width of ... more >>>


TR16-094 | 6th June 2016
Guillaume Lagarde, Guillaume Malod

Non-commutative computations: lower bounds and polynomial identity testing

Comments: 1

In the setting of non-commutative arithmetic computations, we define a class of circuits that gener-
alize algebraic branching programs (ABP). This model is called unambiguous because it captures the
polynomials in which all monomials are computed in a similar way (that is, all the parse trees are iso-
morphic).
We ... more >>>


TR17-077 | 30th April 2017
Guillaume Lagarde, Nutan Limaye, Srikanth Srinivasan

Lower Bounds and PIT for Non-Commutative Arithmetic circuits with Restricted Parse Trees

We investigate the power of Non-commutative Arithmetic Circuits, which compute polynomials over the free non-commutative polynomial ring $\mathbb{F}\langle x_1,\dots,x_N \rangle$, where variables do not commute. We consider circuits that are restricted in the ways in which they can compute monomials: this can be seen as restricting the families of parse ... more >>>


TR19-114 | 2nd September 2019
Visu Makam, Avi Wigderson

Singular tuples of matrices is not a null cone (and, the symmetries of algebraic varieties)

The following multi-determinantal algebraic variety plays a central role in algebra, algebraic geometry and computational complexity theory: ${\rm SING}_{n,m}$, consisting of all $m$-tuples of $n\times n$ complex matrices which span only singular matrices. In particular, an efficient deterministic algorithm testing membership in ${\rm SING}_{n,m}$ will imply super-polynomial circuit lower bounds, ... more >>>




ISSN 1433-8092 | Imprint