On the Parameterized Complexity of Default Logic and Autoepistemic Logic

We investigate the application of Courcelle's Theorem and the logspace version of Elberfeld etal. in the context of the implication problem for propositional sets of formulae, the extension existence problem for default logic, as well as the expansion existence problem for autoepistemic logic and obtain fixed-parameter time and space efficient algorithms for these problems. On the other hand, we exhibit, for each of the above problems, families of instances of a very simple structure that, for a wide range of different parameterizations, do not have efficient fixed-parameter algorithms (even in the sense of the large class XPnu), unless P=NP.Comment: 12 pages + 2 pages appendix, 1 figure, Version without Appendix submitted to LATA 201

Parameterized Complexity of CTL: A Generalization of Courcelle's Theorem

We present an almost complete classification of the parameterized complexity of all operator fragments of the satisfiability problem in computation tree logic CTL. The investigated parameterization is the sum of temporal depth and structural pathwidth. The classification shows a dichotomy between W[1]-hard and fixed-parameter tractable fragments. The only real operator fragment which is confirmed to be in FPT is the fragment containing solely AX. Also we prove a generalization of Courcelle's theorem to infinite signatures which will be used to proof the FPT-membership case.Comment: Conference version: "L\"uck, Meier, Schindler. Parameterized Complexity of CTL: A Generalization of Courcelle's Theorem. Language and Automata Theory and Applications - 9th International Conference, LATA 2015, Nice, France. Lecture Notes in Computer Science, Volume 8977, pp. 549-560, Springer