Parameterised complexity of model checking and satisfiability in propositional dependence logic
Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of PDL is NP -complete (Ebbing and Lohmann, SOFSEM 2012). The subj...
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Published in | Annals of mathematics and artificial intelligence Vol. 90; no. 2-3; pp. 271 - 296 |
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Main Authors | , |
Format | Journal Article |
Language | English |
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ISSN | 1012-2443 1573-7470 |
DOI | 10.1007/s10472-021-09730-w |
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Abstract | Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic
(PDL)
and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of
PDL
is
NP
-complete (Ebbing and Lohmann, SOFSEM 2012). The subject of this research is to identify a list of parameterisations (formula-size, formula-depth, treewidth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) which classically is known to be
NP
-complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT is
paraNP
-complete whereas under all other mentioned parameters the problem is
FPT
. Finally, we introduce a variant of the satisfiability problem, asking for a team of a given size, and show for this problem an almost complete picture. |
---|---|
AbstractList | Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic
(PDL)
and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of
PDL
is
NP
-complete (Ebbing and Lohmann, SOFSEM 2012). The subject of this research is to identify a list of parameterisations (formula-size, formula-depth, treewidth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) which classically is known to be
NP
-complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT is
paraNP
-complete whereas under all other mentioned parameters the problem is
FPT
. Finally, we introduce a variant of the satisfiability problem, asking for a team of a given size, and show for this problem an almost complete picture. Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of PDL is NP-complete (Ebbing and Lohmann, SOFSEM 2012). The subject of this research is to identify a list of parameterisations (formula-size, formula-depth, treewidth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) which classically is known to be NP-complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is FPT. Finally, we introduce a variant of the satisfiability problem, asking for a team of a given size, and show for this problem an almost complete picture. Dependence Logic was introduced by Jouko Vaananen in 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of PDL is NP-complete (Ebbing and Lohmann, SOFSEM 2012). The subject of this research is to identify a list of parameterisations (formula-size, formula-depth, treewidth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) which classically is known to be NP-complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is FPT. Finally, we introduce a variant of the satisfiability problem, asking for a team of a given size, and show for this problem an almost complete picture. Keywords Propositional dependence logic * Parameterised complexity * Model checking * Satisfiability |
Audience | Academic |
Author | Mahmood, Yasir Meier, Arne |
Author_xml | – sequence: 1 givenname: Yasir orcidid: 0000-0002-5651-5391 surname: Mahmood fullname: Mahmood, Yasir email: mahmood@thi.uni-hannover.de organization: Institut für Theoretische Informatik, Leibniz Universität Hannover – sequence: 2 givenname: Arne surname: Meier fullname: Meier, Arne organization: Institut für Theoretische Informatik, Leibniz Universität Hannover |
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Snippet | Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic
(PDL)
and investigate a variety of parameterisations... Dependence Logic was introduced by Jouko Vaananen in 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parameterisations... Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parameterisations... |
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SubjectTerms | Artificial Intelligence Atomic properties Complex Systems Computer Science Logic Mathematical models Mathematics Parameters Semantics Teams |
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Title | Parameterised complexity of model checking and satisfiability in propositional dependence logic |
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