The threshold for random $k$-SAT is $2^k\log 2-O(k)$
نویسندگان
چکیده
منابع مشابه
The Threshold for Random k - SAT is 2 k log 2 − O ( k )
Let Fk(n, m) be a random k-CNF formula formed by selecting uniformly and independently m out of all possible k-clauses on n variables. It is well-known that if r ≥ 2 log 2, then Fk(n, rn) is unsatisfiable with probability that tends to 1 as n → ∞. We prove that if r ≤ 2 log 2 − tk, where tk = O(k), then Fk(n, rn) is satisfiable with probability that tends to 1 as n → ∞. Our technique, in fact, ...
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Let Fk(n, m) be a random k-SAT formula with n variables and m clauses selected uniformly andindependently among all 2(nk)possible k-clauses. It is well-known that if r ≥ 2 ln 2 then Fk(n, rn) isunsatisfiable with probability 1 − o(1). We prove that there exists a sequence tk = O(k) such that ifr ≤ 2 ln 2− tk, then Fk(n, rn) is satisfiable with probability 1− o(1)...
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Form a random k-SAT formula on n variables by selecting uniformly and independently m = rn clauses out of all 2 ( n k ) possible k-clauses. The Satisfiability Threshold Conjecture asserts that for each k there exists a constant rk such that, as n tends to infinity, the probability that the formula is satisfiable tends to 1 if r < rk and to 0 if r > rk . It has long been known that 2/k < rk < 2....
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2004
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-04-00464-3