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Fixed-Parameter Algorithms for Finding Minimal Models

Last modified: 2012-05-17

#### Abstract

Computing minimal models is an important task in Knowledge Representation and Reasoning that appears in formalisms such as circumscription, diagnosis and answer set programming. Even the most basic question of whether there exists a minimal model containing a given variable is known to be $\Sigma_2^P$-complete. In this work we study the problem of computing minimal models from the viewpoint of parameterized complexity theory. We perform an extensive complexity analysis of this problem with respect to eleven parameters. Tractable fragments based on combinations of these parameters are identified by giving several fixed-parameter algorithms. For the remaining combinations we show parameterized hardness results and thus prove that under usual complexity theoretic assumptions no further fixed-parameter algorithms exist for these parameters.

#### Keywords

Satisfiability problem; Minimal models; Parameterized complexity theory; Fixed-parameter algorithms

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