J3/15-153r2
To: J3
From: Tom Clune
Subject: Correct text for definition of ordering of segments
Date: 2015 February 26
References: 15-007
1. Discussion
The text defining user-defined ordering between segments in 8.5.5 is
imprecise, awkwardly worded and inadequate for determining transitive
ordering.
2. Edits to 15-007
[190:38+] Replace text of NOTE 8.29 with
"The set of all segments on all images is partially ordered: the
segment P_i precedes segment Q_j if and only if there is a sequence of
segments S^1_{k_1}, S^2_{k_2}, ..., S^{n}_{k_n} starting with P_i and
ending with Q_j such that each segment S^m_{k_m} of the sequence
precedes the next either because S^{m+1} is the same image as S^m
and k_m < k_{m+1}, or because of the execution of image control
statements synchronizes images S^m and S^{m+1} at the end of segment
S^m_{k_m} and the beginning of S^{m+1}_{k_{m+1}}. This sequence is
not necessarily unique."
[194:1]
Option 1: After "on image P to" insert " immediately"
Option 2: Replace entire line with
"Segment P_i on image P is said to immediately precede segment Q_j on
image Q due to user-defined ordering when"
{Introduce notion of _immediately_ precede and avoid awkward phrasing
in original.}
[194:5] Append new sentence:
"Segment P_i on image P is said to immediately precede segment P_j on
image P if j=i+1. More generally, segment P_i on image P precedes
segment Q_j on image Q if and only if there exists a sequence of
segments S^1_{k_1}, S^2_{k_2}, ..., S^n_{k_n} starting with P_i and
ending with Q_j such that S^m_{k_m} immediately precedes
S^{m+1}_{k_{m+1}} for m = 1, 2, ..., n-1."