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- W51100489 abstract "We investigate phase transitions for the family of bounded satisfiability problems 3SAT(b), recently introduced by Zhang, that ask: given a 3CNF- formula, is there a truth assignment that violates no more than b of its clauses. Zhang's results were experimental and for a fixed number of variables (n = 25), and suggested that the locations of the phase transitions for 3SAT(b) are separated and move significantly as b increases. Analysis of these locations was posed as an open question.We analytically show that the phase transitions of all 3SAT(6) problems must occur within a narrow region, regardless of how large the value of b is. Moreover, our experiments reveal that the phase transitions for these problems occur in a remarkable way. Specifically, unlike 3SAT, the probability curves for 3SAT(6) do not have a quasi-common intersection point about which they rotate as they become steeper with increasing n. Instead, they move rapidly to the left toward the narrow region that the analysis predicts." @default.
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- W51100489 date "2003-08-09" @default.
- W51100489 modified "2023-09-26" @default.
- W51100489 title "Phase transitions of bounded satisfiability problems" @default.
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