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An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>&#8707; Logic

We explore the possibility of automating <i>NP</i>-hardness reductions. We motivate the problem from an artificial intelligence perspective, then propose the use of second-order existential (<i>SO</i>&#8707;) logic as representation language for decision problems. Building upon the theoretical framework of J. Antonio Medina, we explore the possibility of implementing seven syntactic operators. Each operator transforms <i>SO</i>&#8707; sentences in a way that preserves <i>NP</i>-completeness. We subsequently propose a program which implements these operators. We discuss a number of theoretical and practical barriers to this task. We prove that determining whether two <i>SO</i>&#8707; sentences are equivalent is as hard as GRAPH ISOMORPHISM, and prove that determining whether an arbitrary <i>SO</i>&#8707; sentence represents an <i>NP</i>-complete problem is undecidable.

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/1162
Date January 2004
CreatorsNijjar, Paul
PublisherUniversity of Waterloo
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
RightsCopyright: 2004, Nijjar, Paul. All rights reserved.

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