We investigate the application of Courcelle's Theorem and the logspace version of Elberfeld et al. 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 XP nu), unless P = NP. © 2012 Springer-Verlag.
CITATION STYLE
Meier, A., Schmidt, J., Thomas, M., & Vollmer, H. (2012). On the parameterized complexity of default logic and autoepistemic logic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7183 LNCS, pp. 389–400). https://doi.org/10.1007/978-3-642-28332-1_33
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