On the applicability of Post's lattice

@article{Thomas2010OnTA,
  title={On the applicability of Post's lattice},
  author={Michael Thomas},
  journal={Inf. Process. Lett.},
  year={2010},
  volume={112},
  pages={386-391}
}
  • Michael Thomas
  • Published 17 July 2010
  • Mathematics, Computer Science
  • Inf. Process. Lett.

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Parameterized Complexity of Weighted Satisfiability Problems: Decision, Enumeration, Counting

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Complexity of Model Checking for Logics over Kripke models

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T C C C C  N-m L

Michael Thomas and Heribert Vollmer survey in this excellent column recent complexity results for fragments of languages of non-monotonic logics.

References

SHOWING 1-10 OF 33 REFERENCES

The complexity of reasoning for fragments of default logic

This paper systematically restrict the set of allowed propositional connectives and gives a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic.

The Complexity of Circumscriptive Inference in Post’s Lattice

  • Michael Thomas
  • Computer Science, Mathematics
    Theory of Computing Systems
  • 2010
It is shown that in the general case, unless P=NP, only literal theories admit polynomial-time algorithms, while for some restricted variants the tractability border is the same as for classical propositional inference.

The complexity of Boolean formula minimization

The complexity of the original, unbounded depth Minimum Equivalent Expression problem, by showing that the depth-k version is @S"2^P-complete under Turing reductions for all k>=3, is settled.

The Complexity of Problems Defined by Boolean Circuits

A complete collection of (decidable) criteria is presented for the satisfiability problem for boolean circuits with gates from an arbitrary finite base of boolean functions to give a complete characterization of their complexity depending on the base.

The Complexity of Circumscriptive Inference in Post's Lattice

It is shown that in the general case, unless P=NP, only literal theories admit polynomial-time algorithms, while for some restricted variants the tractability border is the same as for classical propositional inference.

The Complexity of Generalized Satisfiability for Linear Temporal Logic

A systematic study of satisfiability for LTL formulae over restricted sets of propositional and temporal operators using Post's lattice to determine the computational complexity of LTL satisfiability.

The Complexity of Model Checking for Boolean Formulas

  • Henning Schnoor
  • Computer Science, Mathematics
    Int. J. Found. Comput. Sci.
  • 2010
The formula model checking problem is either complete for NC1, equivalent to counting modulo 2, or complete for a level of the logarithmic time hierarchy under very strict reductions.

On the Complexity of Some Equivalence Problems for Propositional Calculi

The complexity of Boolean equivalence problems and of Boolean isomorphism problems of two given generalized propositional formulas and certain classes of Boolean circuits are studied.

Satisfiability problems for propositional calculi

  • H. R. Lewis
  • Mathematics, Computer Science
    Mathematical systems theory
  • 2005
It is shown that a condition sufficient for NP-completeness is that the function x Λ ~ y be representable, and that any set of connectives not capable of representing this function has a polynomial-time satisfiability problem.