2] whose sum is k and partial arrays X and Y such that [mathematical expression not reproducible] with row or column catenation.
2]} according to row or column catenation and so, for Z = X, we have AZ [up arrow] [sub.
Section 2 surveys previous work dealing with problems related to that of making lists persistent and adding catenation as an efficient list operation.
Let us put aside catenation for the moment and consider the problem of making noncatenable lists fully persistent.
Once catenation is added as an operation, the problem of making stacks or deques persistent becomes much harder; all the methods mentioned above fail.
The green-yellow-red mechanism applied to an underlying linear structure suffices to add constant-time catenation to stacks.
In this section, we present a real-time, purely functional implementation of deques without catenation.
Our next goal is a deque structure that supports fast catenation.
A catenation of two regular steques takes O(1) time and results in a regular steque.