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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > ALGEBRAIC COMPLEXITY CLASSES:
Reports tagged with Algebraic complexity classes:
TR11-135 | 9th October 2011
Maurice Jansen, Rahul Santhanam

Stronger Lower Bounds and Randomness-Hardness Tradeoffs using Associated Algebraic Complexity Classes

We associate to each Boolean language complexity class $\mathcal{C}$ the algebraic class $a\cdot\mathcal{C}$ consisting of families of polynomials $\{f_n\}$ for which the evaluation problem over the integers is in $\mathcal{C}$. We prove the following lower bound and randomness-to-hardness results:

1. If polynomial identity testing (PIT) is in $NSUBEXP$ then $a\cdot ... more >>>


TR17-087 | 9th May 2017
Pushkar Joglekar, Raghavendra Rao B V, Sidhartha Sivakumar

On Weak-Space Complexity over Complex Numbers

Defining a feasible notion of space over the Blum-Shub-Smale (BSS) model of algebraic computation is a long standing open problem. In an attempt to define a right notion of space complexity for the BSS model, Naurois [CiE, 2007] introduced the notion of weak-space. We investigate the weak-space bounded computations and ... more >>>


TR21-148 | 3rd November 2021
Benjamin Diamond, Amir Yehudayoff

Explicit Exponential Lower Bounds for Exact Hyperplane Covers

We describe an explicit and simple subset of the discrete hypercube which cannot be exactly covered by fewer than exponentially many hyperplanes. The proof exploits a connection to communication complexity, and relies heavily on Razborov's lower bound for disjointness.

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