A note on Dowling and Gallier's top-down algorithm for propositional horn satisfiability
Journal of Logic Programming
Extended Horn sets in propositional logic
Journal of the ACM (JACM)
A Complexity Index for Satisfiability Problems
SIAM Journal on Computing
A linear algorithm for renaming a set of clauses as a Horn set
Theoretical Computer Science
Recognition of q-Horn formulae in linear time
Discrete Applied Mathematics
On finding solutions for extended Horn formulas
Information Processing Letters
A threshold for unsatisfiability
Journal of Computer and System Sciences
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Renaming a Set of Clauses as a Horn Set
Journal of the ACM (JACM)
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Sharp thresholds for certain Ramsey properties of random graphs
Random Structures & Algorithms
Bounded Model Checking Using Satisfiability Solving
Formal Methods in System Design
A perspective on certain polynomial-time solvable classes of satisfiability
Discrete Applied Mathematics
The Asymptotic Order of the Random k -SAT Threshold
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The Probabilistic Analysis of a Greedy Satisfiability Algorithm
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Generalized satisfiability problems: minimal elements and phase transitions
Theoretical Computer Science
Combinatorial sharpness criterion and phase transition classification for random CSPs
Information and Computation
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The sharp Satisfiability threshold is well known for random k-SAT formulas and is due to certain minimality and monotonic properties mentioned in this manuscript and reported in Chandru and Hooker [J. Assoc. Comput. Mach. 38 (1991) 205-221]. Whereas the Satisfiability threshold is on the probability that a satisfying assignment exists, we find that sharp thresholds also may be determined for certain formula structures, for example, the probability that a particular kind of cycle exists in a random formula. Such structures often have a direct relationship on the hardness of a formula because it is often the case that the presence of such a structure disallows a formula from a known, easily solved class of Satisfiability problems. We develop tools that should assist in determining threshold sharpness for a variety of applications. We use the tools to show a sharp threshold for the q-Horn and renameable-Horn properties.