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REPORTS > KEYWORD > FUNCTIONAL LOWER BOUNDS:
Reports tagged with functional lower bounds:
TR21-105 | 22nd July 2021
Suryajith Chillara

Functional lower bounds for restricted arithmetic circuits of depth four

Recently, Forbes, Kumar and Saptharishi [CCC, 2016] proved that there exists an explicit $d^{O(1)}$-variate and degree $d$ polynomial $P_{d} \in VNP$ such that if any depth four circuit $C$ of bounded formal degree $d$ which computes a polynomial of bounded individual degree $O(1)$, that is functionally equivalent to $P_d$, then ... more >>>


TR24-079 | 20th April 2024
Tuomas Hakoniemi , Nutan Limaye, Iddo Tzameret

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers

Strong algebraic proof systems such as IPS (Ideal Proof System; Grochow-Pitassi JACM 2018) offer a general model for
deriving polynomials in an ideal and refuting unsatisfiable propositional formulas, subsuming most standard propositional proof systems. A major approach for lower bounding the size of IPS refutations is the Functional Lower Bound ... more >>>




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