| dc.contributor.author | Nijjar, Paul | en |
| dc.date.accessioned | 2006-08-22 14:28:47 (GMT) | |
| dc.date.available | 2006-08-22 14:28:47 (GMT) | |
| dc.date.issued | 2004 | en |
| dc.date.submitted | 2004 | en |
| dc.identifier.uri | http://hdl.handle.net/10012/1162 | |
| dc.description.abstract | 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. | en |
| dc.format | application/pdf | en |
| dc.format.extent | 539623 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.language.iso | en | en |
| dc.publisher | University of Waterloo | en |
| dc.rights | Copyright: 2004,
Nijjar, Paul. All rights reserved. | en |
| dc.subject | Computer Science | en |
| dc.subject | descriptive complexity | en |
| dc.subject | mathematical discovery | en |
| dc.subject | second-order existential logic | en |
| dc.subject | theorem proving | en |
| dc.title | An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>∃ Logic | en |
| dc.type | Master Thesis | en |
| dc.pending | false | en |
| uws-etd.degree.department | School of Computer Science | en |
| uws-etd.degree | Master of Mathematics | en |
| uws.typeOfResource | Text | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
