• Corpus ID: 2221

On Canonical Forms of Complete Problems via First-order Projections

  title={On Canonical Forms of Complete Problems via First-order Projections},
  author={Nerio Borges and Blai Bonet},
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

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

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



A syntactic characterization of NP-completeness

This paper gives a necessary and sufficient syntactic condition for an SO/spl exist/ formula to represent a problem that is NP-complete via fops and proves syntactically that 29 natural NP- complete problems remain complete via fop.

A descriptive approach to the class NP

This dissertation studies the sentences that express properties that are complete for the class NP via first-order projections (fops), the development of syntactic tools for proving problems NP-complete via fops, the definition of Syntactic families of problems that have a similar syntactic structure, the study of the approximability of the problems in the syntactic families that are defined, and a descriptive version of the PCP theorem.

Generalized first-order spectra, and polynomial. time recognizable sets

The spectrum of a first-order sentence σ is the set of cardinalities of its finite models. Jones and Selman showed that a set C of numbers (written in binary) is a spectrum if and only if C is in the

Capturing Complexity Classes by Fragments of Second-Order Logic

An Attempt to Automate NP -Hardness Reductions via SO ∃ Logic

The problem is motivated from an artificial intelligence perspective, then the use of second-order existential (SO∃) logic as representation language for decision problems is proposed and the possibility of implementing seven syntactic operators is explored, which each transforms SO∃ sentences in a way that preserves NP-completeness.

Computational complexity

Computational complexity is the realm of mathematical models and techniques for establishing impossibility proofs for proving formally that there can be no algorithm for the given problem which runs faster than the current one.

Descriptive Complexity

  • N. Immerman
  • Computer Science
    Graduate Texts in Computer Science
  • 1999
The core of the book is contained in Chapters 1 through 7, although even here some sections can be omitted according to the taste and interests of the instructor, and the remaining chapters are more independent of each other.

Reduction to NP-complete problems by interpretations

A First-Order Isomorphism Theorem

We show that for most complexity classes of interest, all sets complete under first-order projections are isomorphic under first-order isomorphisms. That is, a very restricted version of the

Reducibility by algebraic projections. L'Ensignment Mathématique

  • Reducibility by algebraic projections. L'Ensignment Mathématique
  • 1982