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>∃) 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>∃ 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>∃ sentences are equivalent is as hard as GRAPH ISOMORPHISM, and prove that determining whether an arbitrary <i>SO</i>∃ sentence represents an <i>NP</i>-complete problem is undecidable.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/1162 |
| Date | January 2004 |
| Creators | Nijjar, Paul |
| Publisher | University of Waterloo |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | application/pdf, 539623 bytes, application/pdf |
| Rights | Copyright: 2004, Nijjar, Paul. All rights reserved. |
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