J3/15-153r1 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}_{k_{m+1}} is the same image 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 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 "