Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
Minimal representation of directed hypergraphs
SIAM Journal on Computing
The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
SIAM Journal on Computing
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
On subclasses of minimal unsatisfiable formulas
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
Theoretical Computer Science
Redundancy in logic II: 2CNF and Horn propositional formulae
Artificial Intelligence
Redundancy in logic III: Non-monotonic reasoning
Artificial Intelligence
Variable minimal unsatisfiability
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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Inspired by the notion of minimal unsatisfiable formulae we first introduce and study the class of clause minimal formulae. A CNF formula F is said to be clause minimal if any proper subformula of F is not equivalent to F. We investigate the equivalence and extension problems for clause minimal formulae. The extension problem is the question whether for two formulae F and H there is some formula G such that F+G is equivalent to H. Generally, we show that these problems are intractable. Then we discuss the complexity of these problems restricted by various parameters and constraints. In the last section we ask several open questions in this area.