First-Order Reasoning and Efficient Semi-Algebraic Proofs

@article{Part2021FirstOrderRA,
  title={First-Order Reasoning and Efficient Semi-Algebraic Proofs},
  author={Fedor Part and Neil Thapen and Iddo Tzameret},
  journal={2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
  year={2021},
  pages={1-13}
}
Semi-algebraic proof systems such as sum-of-squares (SoS) have attracted a lot of attention recently due to their relation to approximation algorithms [3]: constant degree semi-algebraic proofs lead to conjecturally optimal polynomial-time approximation algorithms for important NP-hard optimization problems (cf. [4]). Motivated by the need to allow a more streamlined and uniform framework for working with SoS proofs than the restrictive propositional level, we initiate a systematic first-order… 

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