Information Technology Reference
In-Depth Information
Example 10.1
For the bulk-action transaction
T
D
BR
Œs
X
;s
XV
I Œs
0
XV
C
with s
XV
Df
.x
1
;
v
1
/;:::;.x
n
;
v
n
/
g
and s
0
XV
Df
.y
1
;
w
1
/;:::;.y
m
;
w
m
/
g
, possible
states include
BR
Œx
1
;
v
1
:::RŒx
i
;
v
i
,
BR
Œx
1
;
v
1
:::RŒx
n
;
v
n
I Œy
1
;
w
1
:::IŒy
j
;
w
j
,
BR
Œx
1
;
v
1
:::RŒx
n
;
v
n
I Œy
1
;
w
1
:::IŒy
m
;
w
m
C ,
BR
Œx
1
;
v
1
:::RŒx
n
;
v
n
I Œy
1
;
w
1
:::IŒy
j
;
w
j
AI
1
Œy
j
;
w
j
:::I
1
Œy
j
0
;
w
j
0
,
BR
Œx
1
;
v
1
:::RŒx
n
;
v
n
I Œy
1
;
w
1
:::IŒy
j
;
w
j
AI
1
Œy
j
;
w
j
:::I
1
Œy
1
;
w
1
C ,
where i
n, j
0
j
m, x
k
<x
kC1
for k
D
1;:::;n
1,andy
k
<y
kC1
for
k
D
1;:::;m
1.
t
Concurrency of bulk-action transactions is similarly modeled with
expanded
histories
, that is, shuffles of expanded transaction states, thus allowing concurrency
within bulk actions. However, for representing isolation anomalies between bulk-
action transactions via expanded transaction histories, the above mapping of
bulk-read actions is inadequate.
Example 10.2
Assume that the database r is empty initially. In the history
T
1
W
BR
Œ
f
Œ1; 3
g
;
;
:::
T
2
W
BI
Œ
f
.2;
v
/
g
:::
the bulk-read action by T
1
should be considered an unrepeatable read, although no
read action appears in the corresponding expanded history. Similarly, in the history
T
0
1
W
BR
Œ
f
Œ1; 3
g
;
;
:::
T
0
2
W
BD
Œ
f
Œ2; 2
g
;
f
.2;
v
/
g
:::
with r
Df
.2;
v
/
g
initially, the bulk-read action by T
0
1
should be considered a dirty
read.
t
For reducing the definitions of isolation anomalies between bulk-action trans-
actions to those between transactions in the key-range model, we map bulk-read
actions RŒs
X
;s
XV
as follows. Each key range .
z
1
;
z
2
/, Œ
z
1
;
z
2
, .
z
1
;
z
2
,orŒ
z
1
;
z
2
/ in
s
X
is mapped to the sequence of key-range-read actions
RŒx
1
;
z
1
;
v
1
RŒx
2
;>x
1
;
v
2
:::RŒx
k
;>x
k1
;
v
k
RŒx
kC1
;>x
k
;
v
kC1
,
where x
1
;x
2
;:::;x
k
are the keys in the range to be read, and the last action,
RŒx
kC1
;> x
k
;
v
kC1
, is only present if x
k
<
z
2
. In the case RŒx
kC1
;> x
k
;
v
kC1
is present, its output is not considered to be part of the output of RŒs
X
;s
XV
.The
comparison operator is either > or
depending on whether the range to be
read is open or closed on the left end. In the special case that there are no keys
in the range read, the last (and only) action in the mapped sequence is defined to be
RŒx
1
;
z
1
;
v
1
.
