Beyersdorff, O, Meier, A, Thomas, M et al. (1 more author) (2009) The complexity of propositional implication. Information Processing Letters, 109 (18). 1071 - 1077 . ISSN 0020-0190
Abstract
The question whether a set of formulae Γ implies a formula φ is fundamental. The present paper studies the complexity of the above implication problem for propositional formulae that are built from a systematically restricted set of Boolean connectives. We give a complete complexity-theoretic classification for all sets of Boolean functions in the meaning of Post's lattice and show that the implication problem is efficiently solvable only if the connectives are definable using the constants {0,1} and only one of {∧,∨,⊕}. The problem remains coNP-complete in all other cases. We also consider the restriction of Γ to singletons which makes the problem strictly easier in some cases.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Computational complexity, Propositional implication, Post's lattice |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Aug 2012 12:40 |
Last Modified: | 04 Nov 2016 02:10 |
Published Version: | http://dx.doi.org/10.1016/j.ipl.2009.06.015 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.ipl.2009.06.015 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:74442 |