 
Summary: Permuting machines and priority queues
R. E. L. Aldred
M. D. Atkinson
H. P. van Ditmarsch
C. C. Handley
D. A. Holton
D. J. McCaughan
March 31, 2005
Abstract
Machines whose sole function is to reorder their input data are consid
ered. Every such machine defines a set of allowable inputoutput pairs of
permutations. These sets are studied in terms of the minimal disallowed
pairs (the basis). Some allowable sets with small bases are considered
including the one defined by a priority queue machine. For more complex
machines defined by two or more priority queues in series or parallel the
basis is proved to be infinite.
Keywords permutation, pattern, priority queue, basis
1 Introduction
The question of which permutations can be sorted by a stack was posed and
answered by Knuth in [9]. Since then the same question has been studied for
