transactions - backward/forward validation in optimistic concurrency control -

i new "concurrency" & "transactions" , feel little confused backward/forward validation in optimistic concurrency control. take backward validation example. suppose tv transaction being validated , ti committed transactions. wondering why check tv's read set vs.ti's write set . why don't check tv's write set vs.ti's write set , tv's write set vs.ti's read set too? since write-write , write-read conflict operations...any explanation appreciated!

validation uses read-write conflict rules ensure scheduling of particular transaction serially equivalent overlapping transations. means once entered validation phase, no changes read/write sets can further performed.

there 3 rules need satisfied 2 transactions t_i , t_j, < j ( t_i entered validation phase before t_j):

1. t_i must not read objects written t_j

2. t_j must not read objects written t_i

3. t_i must not write objects written t_j , t_j must not write objects written t_i

backward validation assumes read operations of t_i performed before validation of t_j started. means t_i in validation phase. (rule 1 satisfied)

during validation of t_j, read set of t_j checked against write set of t_i. if there no overlap, (rule 2 satisfied).

if rule 1 , rule 2 satified, rule 3 implicitly satisfied. changes commited done sequentially because t_i entered validation phase before t_j. t_i's write set validated , commited before t_j's write set.