Nijjar, Paul2006-08-222006-08-2220042004http://hdl.handle.net/10012/1162We 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.application/pdf539623 bytesapplication/pdfenCopyright: 2004, Nijjar, Paul. All rights reserved.Computer Sciencedescriptive complexitymathematical discoverysecond-order existential logictheorem provingMaster Thesis