Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
Many hard examples for resolution
Journal of the ACM (JACM)
Polynomially solvable satisfiability problems
Information Processing Letters
A note on Dowling and Gallier's top-down algorithm for propositional horn satisfiability
Journal of Logic Programming
Information Sciences: an International Journal
Extended Horn sets in propositional logic
Journal of the ACM (JACM)
A hierarchy of tractable satisfiability problems
Information Processing Letters
On generalized Horn formulas and k-resolution
Theoretical Computer Science
A Complexity Index for Satisfiability Problems
SIAM Journal on Computing
Recognition of q-Horn formulae in linear time
Discrete Applied Mathematics
On finding solutions for extended Horn formulas
Information Processing Letters
Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
A threshold for unsatisfiability
Journal of Computer and System Sciences
On the complexity of unsatisfiability proofs for random k-CNF formulas
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
A Proof Procedure Using Connection Graphs
Journal of the ACM (JACM)
Renaming a Set of Clauses as a Horn Set
Journal of the ACM (JACM)
A short note on some tractable cases of the satisfiability problem
Information and Computation
Investigations on autark assignments
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On the complexity of proof systems
On the complexity of proof systems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The complexity of propositional linear temporal logics in simple cases
Information and Computation
Information Processing Letters
Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
Theoretical Computer Science
Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
Homomorphisms of conjunctive normal forms
Discrete Applied Mathematics - The renesse issue on satisfiability
On Exact Selection of Minimally Unsatisfiable Subformulae
Annals of Mathematics and Artificial Intelligence
Generalizations of Matched CNF Formulas
Annals of Mathematics and Artificial Intelligence
Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable
Journal of Computer and System Sciences
A sharp threshold for the renameable-Horn and the q-Horn properties
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Typical case complexity of satisfiability algorithms and the threshold phenomenon
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Resolution complexity of random constraint satisfaction problems: another half of the story
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Filter-based resolution principle for lattice-valued propositional logic LP(X)
Information Sciences: an International Journal
Linear CNF formulas and satisfiability
Discrete Applied Mathematics
Consistency and random constraint satisfaction models
Journal of Artificial Intelligence Research
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Resolution complexity of random constraint satisfaction problems: Another half of the story
Discrete Applied Mathematics
A sharp threshold for the renameable-Horn and the q-Horn properties
Discrete Applied Mathematics
Typical case complexity of Satisfiability Algorithms and the threshold phenomenon
Discrete Applied Mathematics
Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Matched formulas and backdoor sets
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
A CNF formula hierarchy over the hypercube
AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
A CNF class generalizing exact linear formulas
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Variable minimal unsatisfiability
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Constraint Satisfaction Problems in Clausal Form I: Autarkies and Deficiency
Fundamenta Informaticae
Upper and lower bounds for weak backdoor set detection
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Complexity issues related to propagation completeness
Artificial Intelligence
Generalising Unit-Refutation Completeness and SLUR via Nested Input Resolution
Journal of Automated Reasoning
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The scope of certain well-studied polynomial-time solvable classes of Satisfiability is investigated relative to a polynomial-time solvable class consisting of what we call matched formulas. The class of matched formulas has not been studied in the literature, probably because it seems not to contain many challenging formulas. Yet, we find that, in some sense, the matched formulas are more numerous than Horn, extended Horn, renamable Horn, q-Horn, CC-balanced, or single lookahead unit resolution (SLUR) formulas.The behavior of random k-CNF formulas generated by the constant clause-width model is investigated as n and m, the numbers of variables and clauses, go to infinity. For m/n - 1), the probability that a random formula is SLUR, q-Horn, extended Horn, CC-balanced, or renamable Horn tends to 0. For m/n 0.64, random formulas are matched formulas with probability tending to 1. For m/nk-1 ≥ 2k/k!, random formulas are solved by a certain polynomial-time resolution procedure with probability tending to 1.The propositional connection graph is introduced to represent clause structure for formulas with general-width clauses. Cyclic substructures are exhibited that occur with high probability and prevent formulas from being in the previously studied polynomial-time solvable classes, but do not prevent them from being in the matched class. We believe that part of the significance of this work lies in guiding the future development of polynomial-time solvable classes of Satisfiability.