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1,167 claims from 736 papers are on the record. 43 have been checked so far; the other 1,124 have no check with a result yet.

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Status: Unchecked ×Keyword: k-SAT ×Clear all

10 claims from 6 papers

1. Mathematics › Limits and Structures in Graph Theory

   Sharp thresholds of graph properties, and the $k$-sat problem

   Friedgut and Bourgain · Journal of the American Mathematical Society · 1999

   The paper links the threshold behaviour of monotone random graph properties to approximation by small subgraph lists, and applies this to the satisfiability of random k-CNF formulas.

   Unchecked3 claims
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   1. UncheckedThe paper uses its main theorem to settle whether random k-CNF formulas have a sharp threshold for satisfiability.“As an application of the main theorem we settle the question of the existence of a sharp threshold for the satisfiability of a random $k$-CNF formula.”
   2. Unchecked“We show that if $d\mu _p(P)/dp$ is small (corresponding to a non-sharp threshold), then there is a list of graphs of bounded size such that $P$ can be approximated by the property of having one of the graphs as a subgraph.”
   3. Unchecked“One striking consequence of this result is that a coarse threshold for a random graph property can only happen when the value of the critical edge probability is a rational power of $n$.”

2. Computer Science › Constraint Satisfaction and Optimization

   Where the really hard problems are

   Cheeseman, Kanefsky and Taylor · 1991

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   1. Unchecked“It is the high density of well-separated almost solutions (local minima) at this boundary that cause search algorithms to "thrash".”

3. Computer Science › Constraint Satisfaction and Optimization

   Approximating the unsatisfiability threshold of random formulas

   Kirousis, Kranakis, Kriz̧anc and Stamatiou · Random Structures and Algorithms · 1998

   Unchecked2 claims
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   1. Unchecked“By letting the expected value of the first term of the sequence converge to zero, we obtain, by simple and elementary computations, an upper bound for κ equal to 4.667.”
   2. Unchecked“This technique generalizes in a straightforward manner to k-SAT for k>3.”

4. Computer Science › Constraint Satisfaction and Optimization

   Algorithmic Barriers from Phase Transitions

   Achlioptas and Coja‐Oghlan · 2013

   Unchecked2 claims
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   1. Unchecked“We prove that the factor of 2 corresponds in a precise mathematical sense to a phase transition in the geometry of this set.”
   2. Unchecked“To prove our results we develop a general technique that allows us to prove rigorously much of the celebrated 1-step Replica-Symmetry-Breaking hypothesis of statistical physics for random CSPs.”

5. Computer Science › Constraint Satisfaction and Optimization

   Phase transitions of the typical algorithmic complexity of the random satisfiability problem studied with linear programming

   Schawe, Bleim and Hartmann · PLoS ONE · 2019

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   1. Unchecked“For the present random $K$-SAT problem we have investigated numerous structural properties also exhibiting clear transitions, but they appear not be correlated to the here observed easy-hard transitions.”

6. Computer Science › Constraint Satisfaction and Optimization

   2+p-SAT: Relation of Typical-Case Complexity to the Nature of the Phase Transition

   Monasson, Zecchina, Kirkpatrick, Selman and Troyansky · arXiv (Cornell University) · 1999

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   1. Unchecked“The random first order transition combines properties of the 1st order (discontinuous onset of order) and 2nd order (with power law scaling, e.g. of the width of the the critical region in a finite system) transitions known in the physics of pure solids.”