We describe parameterized complexity classes by means of classical complexity theory and descriptive complexity theory. For every classical complexity class we introduce a parameterized analogue in a natural way. In particular, the analogue of polynomial time is the class of all fixed-parameter tractable problems. We develop a basic complexity theory for the parameterized analogues of classical complexity classes and give, among other things, complete problems and logical descriptions. We then show that most of the well-known intractable parameterized complexity classes are not analogues of classical classes. Nevertheless, for all these classes we can provide natural logical descriptions.
CITATION STYLE
Flum, J., & Grohe, M. (2002). Describing parameterized complexity classes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2285, pp. 359–371). Springer Verlag. https://doi.org/10.1007/3-540-45841-7_29
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