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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 ,
CHARLES KNESSL  and
WOJCIECH SZPANKOWSKI
PHILIPPE JACQUET
Affiliation:
Bell Labs, Alcatel-Lucent, 91620 Nozay, France (e-mail: philippe.jacquet@inria.fr)
CHARLES KNESSL
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA (e-mail: knessl@uic.edu)
WOJCIECH SZPANKOWSKI
Affiliation:
Department of Computer Science, Purdue University, W. Lafayette, IN 47907, USA (e-mail: spa@cs.purdue.edu)
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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

Primary 68W40
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 5: Honouring the Memory of Philippe Flajolet - Part 1 , September 2014 , pp. 829 - 841
Copyright
Copyright © Cambridge University Press 2014 

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References

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