Information Technology Reference
In-Depth Information
Example 5.10
The action R
1
Œx by transaction T
1
is an unrepeatable read in the
histories
B
1
:::R
1
Œx:::B
2
:::W
2
Œx:::C
1
::: ,
B
1
:::R
1
Œx:::B
2
:::D
2
Œx:::C
1
::: ,
assuming that T
1
is still forward-rolling when transaction T
2
performs its update
action. The predicate P in the definition is “X
D
x.”
The read action R
1
Œx is called unrepeatable, because repeating it in T
1
after the
commit of T
2
may be impossible: after W
2
Œx the action RŒx is likely to produce a
tuple with a value different from that obtained in the first reading, and after D
2
Œx,
the action RŒx;
x is impossible, and the action RŒx
0
;
z
will produce a tuple with
key x
0
different from x. It is a natural requirement that if T
1
does not itself update
the tuple with key x in the interim, then the read action RŒx should be repeatable
within T
1
.
The above histories represent the simple type of an unrepeatable read in which
the key updated is the key read.
t
Example 5.11
The action R
1
Œx; >
z
by transaction T
1
is an unrepeatable read in the
history
B
1
:::R
1
Œx; >
z
:::B
2
:::I
2
Œy:::C
1
::: ,
if x>y>
z
, assuming that T
1
is still forward-rolling when transaction T
2
performs
its insert action. The predicate P in the definition is “x
X>
z
.”
The above history exhibits an unrepeatable read of type
phantom phenomenon
.
The tuple with key y that appears into the key range .
z
;x due to the insert action
by T
2
is called a
phantom tuple
.
t
We say that a transaction T in history H
D
˛LJ is
forward-rolling
(resp.
aborted
,
backward-rolling
,
committed
,
rolled-back
,
active
,or
terminated
)
at
˛,if
the prefix T
0
of T contained in ˛ is forward-rolling (resp. aborted, backward-rolling,
committed, rolled-back, active, or terminated) in the history ˛.
For our transaction models (the read-write and key-range model), the isolation
anomalies are defined as follows:
1. An update action o
2
Œx on key x by transaction T
2
is a
dirty write
in history
˛o
2
ŒxLJ,ifx has an uncommitted update by another transaction T
1
in ˛.
2. A read action R
2
Œx;
z
by transaction T
2
is a
dirty read
in history ˛R
2
Œx;
z
LJ,
if some key y with x
y
z
has an uncommitted update by another transaction
T
1
in ˛. The dirty read is a
simple dirty read
if here x
D
y and a
phantom dirty
read
(or a dirty read of type
phantom phenomenon
)ifx>y.
3. A read action R
1
Œx;
z
by transaction T
1
is an
unrepeatable read
in history
˛R
1
Œx;
z
LJo
2
Œy ,ifT
1
is forward-rolling at ˛R
1
Œx;
z
LJ and o
2
Œy is an update
action by another transaction T
2
on key y with x
y
z
. The unrepeatable read
is a
simple unrepeatable read
if here x
D
y and a
phantom unrepeatable read
(or an unrepeatable read of type
phantom phenomenon
)ifx>y.
