Parametrised complexity of satisfiability in temporal logic

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Luck, M.; Meier, A.; Schindler, I.: Parametrised complexity of satisfiability in temporal logic. In: ACM Transactions on Computational Logic 18 (2017), Nr. 1, 1. DOI: https://doi.org/10.1145/3001835

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To cite the version in the repository, please use this identifier: https://doi.org/10.15488/1212

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Sum total of downloads: 192




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Abstract: 
We apply the concept of formula treewidth and pathwidth to computation tree logic, linear temporal logic, and the full branching time logic. Several representations of formulas as graphlike structures are discussed, and corresponding notions of treewidth and pathwidth are introduced. As an application for such structures, we present a classification in terms of parametrised complexity of the satisfiability problem, where we make use of Courcelle's famous theorem for recognition of certain classes of structures. Our classification shows a dichotomy between W[1]-hard and fixed-parameter tractable operator fragments almost independently of the chosen graph representation. The only fragments that are proven to be fixed-parameter tractable (FPT) are those that are restricted to the X operator. By investigating Boolean operator fragments in the sense of Post's lattice, we achieve the same complexity as in the unrestricted case if the set of available Boolean functions can express the function "negation of the implication." Conversely, we show containment in FPT for almost all other clones. © ACM 2017. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in ACM Transactions on Computational Logic 18 (2017), Nr. 1, 1. DOI: https://doi.org/10.1145/3001835.
License of this version: Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Document Type: Text
Publishing status: acceptedVersion
Issue Date: 2017
Appears in Collections:Fakultät für Architektur und Landschaft

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pos. country downloads
total perc.
1 image of flag of Germany Germany 154 80.21%
2 image of flag of Brazil Brazil 7 3.65%
3 image of flag of United States United States 5 2.60%
4 image of flag of No geo information available No geo information available 4 2.08%
5 image of flag of India India 4 2.08%
6 image of flag of China China 4 2.08%
7 image of flag of Japan Japan 2 1.04%
8 image of flag of United Kingdom United Kingdom 2 1.04%
9 image of flag of France France 2 1.04%
10 image of flag of Bulgaria Bulgaria 1 0.52%
    other countries 7 3.65%

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