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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > UTSAB GHOSAL:
All reports by Author Utsab Ghosal:

TR25-098 | 13th July 2025
Prerona Chatterjee, Utsab Ghosal, Partha Mukhopadhyay, Amit Sinhababu

IPS Lower Bounds for Formulas and Sum of1 ROABPs

Revisions: 1

We give new lower bounds for the fragments of the Ideal Proof System (IPS) introduced by Grochow and Pitassi (JACM 2018). The Ideal Proof System is a central topic in algebraic proof complexity developed in the context of Nullstellensatz refutation (Beame, Impagliazzo, Krajicek, Pitassi, Pudlak, FOCS 1994) and simulates Extended ... more >>>


TR22-071 | 13th May 2022
Arkadev Chattopadhyay, Utsab Ghosal, Partha Mukhopadhyay

Robustly Separating the Arithmetic Monotone Hierarchy Via Graph Inner-Product

We establish an $\epsilon$-sensitive hierarchy separation for monotone arithmetic computations. The notion of $\epsilon$-sensitive monotone lower bounds was recently introduced by Hrubes [Computational Complexity'20]. We show the following:

(1) There exists a monotone polynomial over $n$ variables in VNP that cannot be computed by $2^{o(n)}$ size monotone ... more >>>




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