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- W2037281185 abstract "To study the structure of solutions for random k-SAT 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 k-SAT this phenomenon will occur when k⩾5. 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." @default.
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- W2037281185 date "2004-01-01" @default.
- W2037281185 modified "2023-09-26" @default.
- W2037281185 title "On the average similarity degree between solutions of random k-SAT and random CSPs" @default.
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- W2037281185 doi "https://doi.org/10.1016/s0166-218x(03)00204-x" @default.
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