## 9 Citations

### Parameterized Complexity of Weighted Satisfiability Problems

- MathematicsSAT
- 2012

All fragments obtained by semantically restricting circuits or formulae to contain only gates (connectives) from a fixed set B of Boolean functions are considered and a dichotomy result is obtained by showing that for each such B, the weighted satisfiability problems are either W[P]-complete or W[SAT]-complete (for circuits) or efficiently solvable.

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

- MathematicsFundam. Informaticae
- 2015

All fragments obtained by semantically restricting circuits or formulae to contain only gates (connectives) from a fixed set B of Boolean functions are considered and a dichotomy result is obtained by showing that for each such B, the weighted satisfiability problems are either W[P]-complete or W[SAT]-complete (for circuits) or efficiently solvable.

### Model Checking for Modal Dependence Logic: An Approach through Post's Lattice

- Computer ScienceWoLLIC
- 2013

An extended version of modal dependence logic by allowing arbitrary Boolean connectives is investigated and the computational complexity of the model checking problem is studied.

### The Connectivity of Boolean Satisfiability: Dichotomies for Formulas and Circuits

- Mathematics, Computer ScienceTheory of Computing Systems
- 2015

Connectivity issues of satisfiability problems defined by Boolean circuits and propositional formulas that use gates, resp.

### Complexity of non-monotonic logics

- Computer ScienceBull. EATCS
- 2010

This survey considers a logical formalism from each of the above possibilities, namely Reiter's default logic, Moore's autoepistemic logic and McCarthy's circumscription, and describes complexity results for fragments of logical languages obtained by restricting the allowed set of operators.

### Connectivity of Boolean satisfiability

- MathematicsArXiv
- 2015

A computational dichotomy is proved for the st-connectivity problem, asserting that it is either solvable in polynomial time or PSPACE-complete, and an aligned structural dichotomy for the connectivity problem is proved, asserting the maximal diameter of connected components is either linear in the number of variables, or can be exponential.

### Complexity of Model Checking for Logics over Kripke models

- Computer ScienceBull. EATCS
- 2012

In their excellent and detailed survey, the authors bring out the intricate structures involved in the reductions and the effectiveness of standard complexity classes in capturing the complexity of model checking.

### T C C C C N-m L

- Computer Science
- 2010

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

## References

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- PhilosophyJ. Log. Comput.
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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

- Computer Science, MathematicsTheory of Computing Systems
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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

- Computer ScienceJ. Comput. Syst. Sci.
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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

- Mathematics, Computer Science
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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

- Computer ScienceLPNMR
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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

- MathematicsElectron. Colloquium Comput. Complex.
- 2006

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

- Computer Science, MathematicsInt. 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

- Mathematics, PhilosophyMFCS
- 2003

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

- Mathematics, Computer ScienceMathematical 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.