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A Note on a Problem Posed by D. E. Knuth on a Satisfiability Recurrence

Published online by Cambridge University Press:  09 July 2014

PHILIPPE JACQUET
Affiliation:
Bell Labs, Alcatel-Lucent, 91620 Nozay, France (e-mail: [email protected])
CHARLES KNESSL
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA (e-mail: [email protected])
WOJCIECH SZPANKOWSKI
Affiliation:
Department of Computer Science, Purdue University, W. Lafayette, IN 47907, USA (e-mail: [email protected])

Abstract

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.

Keywords

Type
Paper
Copyright
Copyright © Cambridge University Press 2014 

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