Parameterised complexity of model checking and satisfiability in propositional dependence logic

• Published in: Annals of mathematics and artificial intelligence Vol. 90; no. 2-3; pp. 271 - 296
• Main Authors: Mahmood, Yasir, Meier, Arne
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2022; Springer; Springer Nature B.V
• Subjects: Artificial Intelligence; Atomic properties; Complex Systems; Computer Science; Logic; Mathematical models; Mathematics; Parameters; Semantics; Teams; Model checking; 68Q25; Propositional dependence logic; 03B70; Parameterised complexity; Satisfiability
• ISSN: 1012-2443; 1573-7470
• DOI: 10.1007/s10472-021-09730-w

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.