The 3-XORSAT Threshold

Abstract : We prove the existence of a threshold phenomenon regarding the random 3-XORSAT problem (or more generally k-XORSAT). We provide the value of the threshold as the solution of two transcendental equations. These results confirm rigorously those obtained by physicists using the one-step replica symmetry breaking method and thus give for the first time the proof of the validity of this method for a problem of the class of satisfiability problems.
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Olivier Dubois, Jacques Mandler. The 3-XORSAT Threshold. Comptes Rendus Mathématique, Elsevier Masson, 2002, 335 (11), pp.963-966. ⟨10.1016/S1631-073X(02)02563-3⟩. ⟨hal-01185801⟩



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