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Algorithms and Complexity Results for Input and Unit Resolution

Article type: Research Article

Authors: Hertel, Alexander; * | Urquhart, Alasdair

Affiliations: Department of Computer Science, University of Toronto, Canada. E-mails: ahertel@cs.toronto.edu, urquhart@cs.toronto.edu

Note: [*] The authors gratefully acknowledge NSERC and the University of Toronto Department of Computer Science for supporting this research.

Keywords: satisfiability, complexity, resolution, input resolution

DOI: 10.3233/SAT190066

Journal: Journal on Satisfiability, Boolean Modeling and Computation, vol. 6, no. 1-3, pp. 141-164, 2010

Received 1 November 2007
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Revision received 1 June 2008
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Published: 1 May 2009
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Abstract

In this paper we explore the complexity of various problems pertaining to Input Resolution. In the first part of this paper we survey a number of earlier results for Input Resolution, showing the tractability of various aspects of this proof system. In the second part, we prove the PSPACE-Completeness of both Input Resolution total space and width, as well as a massive size/total space tradeoff for Input Resolution. These results suggest that although Input Resolution is completely tractable with respect to certain complexity measures such as refutation size, when quantities such as space and width are considered, the system shows a surprising level of difficulty.

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