A Note on a Problem Posed by D. E. Knuth on a Satisfiability Recurrence. (September 2014) - JACQUET, PHILIPPE; KNESSL, CHARLES; SZPANKOWSKI, WOJCIECH; Broutin, Nicolas; Fill, James Allen; Nebel, Markus; Ward, Mark Daniel
<x content-type="archive" xml:space="preserve">Abstract</x> We resolve a conjecture proposed by D.E. Knuth concerning a recurrence arising in the satisfiability problem. Knuth's recurrence resembles recurrences arising in the analysis of tries, in particular PATRICIA tries, and asymmetric leader election. We solve Knuth's recurrence exactly and asymptotically, using analytic techniques such as the Mellin transform and analytic depoissonization.