Lower bounds for monotone arithmetic circuits via communication complexity

Chattopadhyay, Arkadev; Datta, Rajit; Mukhopadhyay, Partha

doi:10.1145/3406325.3451069

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Extending the Techniques Of Hrubeš And Yehudayoff1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

2023

Publication Types

Select...

Other3

Article2

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 5 publications

(2 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A similar lower bound for an even simpler polynomial was proved by Hrubeš and Yehudayoff [24]. Unfortunately, these results do not seem to imply general formula or circuit lower bounds, as it is not clear how to efficiently convert a general algebraic circuit or formula to a monotone one: in fact, there is strong indication that this might be impossible [61,8,7].…”

Section: Introductionmentioning

confidence: 69%

Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits

Limaye

Srinivasan

Tavenas

2022

2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 69%

Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits

Limaye

Srinivasan

Tavenas

2022

2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)

View full text Add to dashboard Cite

show abstract

“…Further, if transparent polynomials also happen to be hard for mVPSPACE as we believe, then a transparent polynomial in VP would essentially show that VP ⊂ mVPSPACE. Even though stark separations between monotone and non-monotone models are not unheard of [HY13,CDM21], such a result would be very interesting, and would further highlight the power of subtractions.…”

Section: Extending the Techniques Of Hrubeš And Yehudayoffmentioning

confidence: 99%

Transparency Beyond VNP in the Monotone Setting

Chatterjee¹,

Gajjar²,

Tengse³

2022

Preprint

View full text Add to dashboard Cite

Recently Hrubeš and Yehudayoff [HY21] showed a connection between the monotone algebraic circuit complexity of transparent polynomials and a geometric complexity measure of their Newton polytope. They then used this connection to prove lower bounds against monotone VP (mVP). We extend their work by showing that their technique can be used to prove lower bounds against classes that are seemingly more powerful than monotone VNP (mVNP).In the process, we define a natural monotone analogue of VPSPACE -a well-studied class in the non-monotone setting [Poi08, KP09, Mal11, MR13] -and prove an exponential separation between the computational powers of this class and mVNP.To show this separation, we define a new polynomial family with an interesting combinatorial structure which we use heavily in our lower bound. Both the polynomial and the combinatorial nature of our proof might be of independent interest.

show abstract