
The SAT Phase Transition
Phase transition is an important feature of SAT problem. For random kSA...
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Super Solutions of the Model RB
The concept of super solution is a special type of generalized solutions...
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An Average Analysis of Backtracking on Random Constraint Satisfaction Problems
In this paper we propose a random CSP model, called Model GB, which is a...
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The birth of the contradictory component in random 2SAT
We prove that, with high probability, the contradictory components of a ...
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Percolation and Phase Transition in SAT
Erdös and Rényi proved in 1960 that a drastic change occurs in a large r...
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Satisfiability Threshold for Power Law Random 2SAT in Configuration Model
The Random Satisfiability problem has been intensively studied for decad...
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Locality of Random Digraphs on Expanders
We study random digraphs on sequences of expanders with bounded average ...
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On the Average Similarity Degree between Solutions of Random kSAT and Random CSPs
To study the structure of solutions for random kSAT and random CSPs, this paper introduces the concept of average similarity degree to characterize how solutions are similar to each other. It is proved that under certain conditions, as r (i.e. the ratio of constraints to variables) increases, the limit of average similarity degree when the number of variables approaches infinity exhibits phase transitions at a threshold point, shifting from a smaller value to a larger value abruptly. For random kSAT this phenomenon will occur when k>4 . It is further shown that this threshold point is also a singular point with respect to r in the asymptotic estimate of the second moment of the number of solutions. Finally, we discuss how this work is helpful to understand the hardness of solving random instances and a possible application of it to the design of search algorithms.
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