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Table 1 Standard notations

From: Inclusive transformation consistency control algorithm in distributed system

Notations Description
o.id Id of site that generate operation o
o.type Type of operation o, i.e., either insert or delete
o.pos Position of operation o
o.str String insert/delete by o
o1 → o2 o1 occurs before o2
o1||o2 o1 and o2 are concurrent
o1Uo2 o1 and o2 are contextually equivalent
o1 → o2 o1 and o2 are contextually serialized
[o1,o2] An ordered list of two operations o1 and o2
<o1,o2> Two operations in sequence
|L| Number of objects in list L
L1.L2 Concatenation of two lists L1 and L2
s [i:len] Substring of string s start from position i of length len
sq A sequence is a special list in which all elements are operations that are contextually serialized
sq = <o1, o2,…, on> sq = <o1, o2,…, on > , where o1 - > o2- > …- > on
< > An empty sequence
L = [a, b, c], it has L = [a]· [b, c] = [a, b]· c A sequence is a special list in which all elements are operations that are contextually serialized
|sq| = n The number of elements in sequence sq = n
sq = < o1 > . < o2,… on > All elements of sequence are contextually serialized
R1 = [o1.start, o1.end] Operation region of operation o1 s R1 which start from o1.start & end at o1.end
o.Substring (i,len) Substring of o start from i of length len
o.Substring (i) Substring of o start from i position in o