Solving homogeneous linear equations over polynomial semirings

@article{Dong2022SolvingHL,
  title={Solving homogeneous linear equations over polynomial semirings},
  author={Rui-Tao Dong},
  journal={ArXiv},
  year={2022},
  volume={abs/2209.13347}
}
For a subset B of R , denote by U( B ) be the semiring of (univariate) polynomials in R [ X ] that are strictly positive on B . Let N [ X ] be the semiring of (univariate) polynomials with non-negative integer coefficients. We study solutions of homogeneous linear equations over the polynomial semirings U( B ) and N [ X ]. In particular, we prove local-global principles for solving single homogeneous linear equations over these semirings. We then show PTIME decidability of determining the… 

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