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

We explore the possibility of automating NP-hardness reductions. We motivate the problem from an artificial intelligence perspective, then propose the use of second-order existential (SO∃) logic as representation language for decision problems. Bui...

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Bibliographic Details
Main Author:	Nijjar, Paul
Language:	en
Published:	University of Waterloo 2006
Subjects:	Computer Science descriptive complexity mathematical discovery second-order existential logic theorem proving
Online Access:	http://hdl.handle.net/10012/1162

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spelling	ndltd-LACETR-oai-collectionscanada.gc.ca-OWTU.10012-11622014-06-18T03:51:12Z An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>∃ Logic Nijjar, Paul Computer Science descriptive complexity mathematical discovery second-order existential logic theorem proving 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. 2006-08-22T14:28:47Z 2006-08-22T14:28:47Z 2004 2004 Thesis or Dissertation http://hdl.handle.net/10012/1162 en Copyright: 2004, Nijjar, Paul. All rights reserved. University of Waterloo
collection	NDLTD
language	en
sources	NDLTD
topic	Computer Science descriptive complexity mathematical discovery second-order existential logic theorem proving
spellingShingle	Computer Science descriptive complexity mathematical discovery second-order existential logic theorem proving Nijjar, Paul An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>∃ Logic
description	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.
author	Nijjar, Paul
author_facet	Nijjar, Paul
author_sort	Nijjar, Paul
title	An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>∃ Logic
title_short	An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>∃ Logic
title_full	An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>∃ Logic
title_fullStr	An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>∃ Logic
title_full_unstemmed	An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>∃ Logic
title_sort	attempt to automate <i>np</i>-hardness reductions via <i>so</i>∃ logic
publisher	University of Waterloo
publishDate	2006
url	http://hdl.handle.net/10012/1162
work_keys_str_mv	AT nijjarpaul anattempttoautomateinpihardnessreductionsviaisoi8707logic AT nijjarpaul attempttoautomateinpihardnessreductionsviaisoi8707logic
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An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>&#8707; Logic

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An Attempt to Automate <i>NP</i>-Hardness Reductions via <i>SO</i>∃ Logic