• Corpus ID: 2221

On Canonical Forms of Complete Problems via First-order Projections

@article{Borges2007OnCF,
  title={On Canonical Forms of Complete Problems via First-order Projections},
  author={Nerio Borges and Blai Bonet},
  journal={ArXiv},
  year={2007},
  volume={abs/0706.3412}
}
The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that defines IndependentSet. This result can also be understood as that every sentence that defines a NP-complete problem P can be decomposed in two disjuncts such that the first one characterizes a fragment of P as hard as IndependentSet and the second the rest… 

A syntactic tool for proving hardness in the Second Level of the Polynomial-Time Hierarchy

TLDR
B Borges and Bonet extend some results from Immerman and Medina and they prove for a host of complexity classes that the Immer man- Medina conjecture is true when the First Order sentence in the conjunc- tion is universal.

Universal first-order logic is superfluous in the second level of the polynomial-time hierarchy

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The superfluity method is interesting since it gives a way to prove completeness of problems involving numerical data such as lengths, weights and costs and it also adds to the programme started by Immerman and Medina about the syntactic approach in the study of completeness.

Completitud en el segundo nivel de la jerarquía polinomial a través de propiedades sintácticas

Pin Baque, Edwin (2016) Completitud en el segundo nivel de la jerarquia polinomial a traves de propiedades sintacticas. Trabajo de Grado presentado ante la Universidad Central de Venezuela para optar

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