{"date_updated":"2023-07-03T11:45:47Z","page":"271-296","issue":"2-3","language":[{"iso":"eng"}],"intvolume":"        90","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic<jats:italic>(PDL)</jats:italic>and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of<jats:italic>PDL</jats:italic>is<jats:bold>NP</jats:bold>-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<jats:bold>NP</jats:bold>-complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT is<jats:bold>paraNP</jats:bold>-complete whereas under all other mentioned parameters the problem is<jats:bold>FPT</jats:bold>. 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.</jats:p>"}],"publication":"Annals of Mathematics and Artificial Intelligence","title":"Parameterised complexity of model checking and satisfiability in propositional dependence logic","user_id":"99353","publication_identifier":{"issn":["1012-2443","1573-7470"]},"year":"2021","author":[{"last_name":"Mahmood","full_name":"Mahmood, Yasir","first_name":"Yasir"},{"first_name":"Arne","last_name":"Meier","full_name":"Meier, Arne"}],"status":"public","_id":"45849","publication_status":"published","doi":"10.1007/s10472-021-09730-w","date_created":"2023-07-03T11:45:39Z","citation":{"apa":"Mahmood, Y., &#38; Meier, A. (2021). Parameterised complexity of model checking and satisfiability in propositional dependence logic. <i>Annals of Mathematics and Artificial Intelligence</i>, <i>90</i>(2–3), 271–296. <a href=\"https://doi.org/10.1007/s10472-021-09730-w\">https://doi.org/10.1007/s10472-021-09730-w</a>","mla":"Mahmood, Yasir, and Arne Meier. “Parameterised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic.” <i>Annals of Mathematics and Artificial Intelligence</i>, vol. 90, no. 2–3, Springer Science and Business Media LLC, 2021, pp. 271–96, doi:<a href=\"https://doi.org/10.1007/s10472-021-09730-w\">10.1007/s10472-021-09730-w</a>.","chicago":"Mahmood, Yasir, and Arne Meier. “Parameterised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic.” <i>Annals of Mathematics and Artificial Intelligence</i> 90, no. 2–3 (2021): 271–96. <a href=\"https://doi.org/10.1007/s10472-021-09730-w\">https://doi.org/10.1007/s10472-021-09730-w</a>.","bibtex":"@article{Mahmood_Meier_2021, title={Parameterised complexity of model checking and satisfiability in propositional dependence logic}, volume={90}, DOI={<a href=\"https://doi.org/10.1007/s10472-021-09730-w\">10.1007/s10472-021-09730-w</a>}, number={2–3}, journal={Annals of Mathematics and Artificial Intelligence}, publisher={Springer Science and Business Media LLC}, author={Mahmood, Yasir and Meier, Arne}, year={2021}, pages={271–296} }","ieee":"Y. Mahmood and A. Meier, “Parameterised complexity of model checking and satisfiability in propositional dependence logic,” <i>Annals of Mathematics and Artificial Intelligence</i>, vol. 90, no. 2–3, pp. 271–296, 2021, doi: <a href=\"https://doi.org/10.1007/s10472-021-09730-w\">10.1007/s10472-021-09730-w</a>.","ama":"Mahmood Y, Meier A. Parameterised complexity of model checking and satisfiability in propositional dependence logic. <i>Annals of Mathematics and Artificial Intelligence</i>. 2021;90(2-3):271-296. doi:<a href=\"https://doi.org/10.1007/s10472-021-09730-w\">10.1007/s10472-021-09730-w</a>","short":"Y. Mahmood, A. Meier, Annals of Mathematics and Artificial Intelligence 90 (2021) 271–296."},"keyword":["Applied Mathematics","Artificial Intelligence"],"type":"journal_article","publisher":"Springer Science and Business Media LLC","volume":90}