D. Achlioptas and C. Moore. The asymptotic order of the random k-SAT threshold. In Proc. 43rd Annual Symposium on Foundations of Computer Science, pages 126--127, 2002. Home/Search Document Details and Download
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The Threshold for Random k-SAT is 2^k log 2 - O(k) - Achlioptas, Peres (2004) Self-citation (Achlioptas) (Correct)
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D. Achlioptas and C. Moore. The asymptotic order of the random k-SAT threshold. In Proc. 43rd Annual Symposium on Foundations of Computer Science, pages 126--127, 2002.
The Fraction of Satisfiable Clauses in a Typical Formula - Achlioptas, Naor, Peres Self-citation (Achlioptas) (Correct)
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Dimitris Achlioptas and Cristopher Moore, The asymptotic order of the random k-SAT threshold, 43th Annual Symposium on Foundations of Computer Science (Vancouver, BC, 2002), pp. 779--788.
On the 2-Colorability of Random Hypergraphs - Achlioptas, Moore (1 citation) Self-citation (Achlioptas Moore) (Correct)
.... Chv atal and Reed [8] In fact, those algorithms give a similar m =k) lower bound on the random k SAT threshold which, like r k , can also be easily bounded as O(2 ) Very recently, the authors eliminated the gap for the random k SAT threshold, determining its value within a factor of two [2]. The proof amounts to applying the second moment method to the set of satisfying truth assignments whose complement is also satisfying. Alternatively, one can think of this as applying the second moment method to the number of truth assignments under which every k clause contains at least one ....
.... moment method to the number of truth assignments under which every k clause contains at least one satis ed literal and at least one unsatis ed literal, i.e. which satisfy the formula when interpreted as a random instance of Not All Equal k SAT (NAE k SAT) Here we extend the techniques of [2] and apply them to hypergraph 2colorability. This allows us to determine r k within a small additive constant. Theorem 1. For every 0 and all k k 0 ( r k 2 ln 2 2 Our method actually yields an explicit lower bound for r k for each value of k as the solution to a simple equation ....
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Achlioptas, D., and Moore, C. The asymptotic order of the random k-SAT threshold. To appear in 43rd Annual Symposium on Foundations of Computer Science (Vancouver, BC, 2002).
The Threshold for Random k-SAT is 2^k (ln 2 + o(1)) - Achlioptas, Peres Self-citation (Achlioptas) (Correct)
....k is arbitrarily large but fixed while n ##. For each k r k = sup r : F k (n, rn) is satisfiable w.h.p. inf r : F k (n, rn) is unsatisfiable w.h.p. r # k . Much work has been done to bound r k , r # k and we survey some of it below. The best bounds prior to our work for general k, from [1] and [8] respectively, di#ered asymptotically by a factor of 2. Specifically, O(1) # r # k ln 2 . The Satisfiability Threshold Conjecture asserts that r k = r # k for all k 3. Our main result establishes an asymptotic form of this conjecture. Theorem 1 r k = r # k (1 o(1) In ....
....random k SAT, e.g. when clause replacement is not allowed and or when each k clause is formed by selecting k literals uniformly at random with replacement. Until very recently, all lower bounds for the random k SAT threshold were algorithmic and of the form #o k) The bound r k O(1) from [1], also derived via a non constructive argument, was the first to break the 2 k barrier. We want to emphasize that we do not view determining r k as an end in itself. Rather, establishing the threshold s asymptotic location clears the field for asking: Can polynomial time algorithms find ....
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D. Achlioptas and C. Moore. The asymptotic order of the random k-SAT threshold. In 43th Annual Symposium on Foundations of Computer Science (Vancouver, BC, 2002.
Hunting for Sharp Thresholds - Friedgut (2004) (Correct)
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D. Achlioptas, C. Moore, The Asymptotic Order of the Random k-SAT Threshold, in Proceedings of FOCS 2002.
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