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About this paper
Omkar Baraskar, Agrim Dewan, Chandan Saha, Pulkit Sinha
The paper demonstrates the NP-hardness of determining if a given polynomial is equivalent to an s-sparse polynomial, resolving a long-standing open question in algebraic complexity. It also establishes the NP-hardness of approximating the sparse-orbit complexity within a super-constant factor for any field and integral domain.
Key insights
- ETsparse is inherently NP-hard over any field, confirming the computational difficulty of testing equivalence for a fundamental class of polynomials.
- The NP-hardness of homogeneous ETsparse directly contributes to the understanding of MCSP for depth-3 arithmetic circuits by proving hardness for a dense subclass of homogeneous ΣΠΣ circuits.
- General and simpler NP-hardness results are achieved for Shift Equivalence Testing (SETsparse) and its approximation over any integral domain, avoiding complex techniques like the PCP theorem.
Summary by alphaXiv.
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