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On The Complexity of Model Checking and Inference in Minimal Models

Extended Abstract
  • Leferis M. Kirousis
  • Phokion G. Kolaitis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2173)

Abstract

Every logical formalism gives rise to two fundamental algorithmic problems: model checking and inference. In propositional logic, the model checking problem is polynomial-time solvable, while the inference problem is coNP-complete. In propositional circumscription, however, these problems have higher computational complexity, namely the model checking problem is coNP-complete, while the inference problem is П P 2 -complete. In this paper, we survey recent results on the computational complexity of restricted cases of these problems in the context of Schaefer’s framework of generalized satisfiability problems. These results establish dichotomies in the complexity of the model checking problem and the inference problem for propositional circumscription. Specifically, in each restricted case the model checking problem for propositional circumscription either is coNP-complete or is polynomial-time solvable. Furthermore, in each restricted case the inference problem for propositional circumscription either is П P 2 -complete or is in coNP. These dichotomy theorems yield a complete classification of the “hard” and the “easier” cases of the model checking problem and the inference problem for propositional circumscription. Moreover, they provide efficiently checkable criteria that tell apart the “hard” cases from the “easier” ones.

Keywords

Model Check Minimal Model Dichotomy Theorem Logical Relation Truth Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Leferis M. Kirousis
    • 1
  • Phokion G. Kolaitis
    • 2
  1. 1.Department of Computer Engineering and InformaticsUniversity of PatrasPatrasGreece
  2. 2.Computer Science DepartmentUniversity of CaliforniaUSA

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