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Describing parameterized complexity classes. (English) Zbl 1076.68031
Summary: 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.

68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
68Q19 Descriptive complexity and finite models
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