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Electronic Colloquium on Computational Complexity

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Reports tagged with polynomial equations:
TR21-112 | 30th July 2021
Vikraman Arvind, Venkatesan Guruswami

CNF Satisfiability in a Subspace and Related Problems

We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the Union-of-Subspace Avoidance (USA) problem), and finding a common zero of a system of ... more >>>

TR22-106 | 21st July 2022
Suryajith Chillara, Coral Grichener, Amir Shpilka

On Hardness of Testing Equivalence to Sparse Polynomials Under Shifts

We say that two given polynomials $f, g \in R[x_1, \ldots, x_n]$, over a ring $R$, are equivalent under shifts if there exists a vector $(a_1, \ldots, a_n)\in R^n$ such that $f(x_1+a_1, \ldots, x_n+a_n) = g(x_1, \ldots, x_n)$. This is a special variant of the polynomial projection problem in Algebraic ... more >>>

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