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(a) A forward-rolling transaction in H cannot be aborted and rolled back if it has
done a dirty read.
(b) H may contain two committed transactions, T
1
and T
2
,whereT
1
commits
before T
2
, although T
2
<T
1
(i.e., T
2
and T
1
conflict and T
2
does the conflicting
action before T
1
in H ).
(c) If H is serializable, then one of the serializability orders of the committed
transactions in H is the
commit order
of those transactions, that is, the order
in which the transactions commit in H .
5.9
Consider the extended read-write transaction model in which a transaction can
use the action CŒx to declare the updates on x done so far as committed before the
transaction terminates (see Problem
1.5
). An update declared as committed becomes
immediately visible to other transactions. Revise the definitions of the isolation
anomalies so as to observe this feature.
5.10
Assume that the tuples .x; y;
v
/ of a relation r.X;Y;V/ can be accessed
besides by the unique primary key x also by the (non-unique) key y (see Prob-
lem
1.6
). Extend the definitions of the isolation anomalies so as to cover read actions
based on non-unique keys.
5.11
Assume that our basic (single-granular) key-range transaction model is
extended to a multi-granular setting with three levels: database, relation, and tuple
(see Sect.
1.10
). Extend accordingly the definitions of isolation anomalies. Observe,
for example, that if transaction T
1
creates a relation r and then transaction T
2
inserts
a tuple into r while T
1
is still active, then the action of T
2
must be termed a dirty
write.
5.12
In an attempt to state a converse for Theorem
5.29
in the case the history
contains several active transactions, we extend the definition of a conflicting pair
of actions so as to observe commit actions as follows. First, the commit actions
C
1
and C
2
of two transactions T
1
and T
2
conflict if T
1
and T
2
contain a pair of
conflicting actions. Second the commit action of T
1
conflicts with an action o
2
Œy of
T
2
if T
1
contains an action o
1
Œx that conflicts with o
2
Œy. Restate Theorem
5.29
for
this extension, still assuming that the history contains no undo actions, and state a
converse theorem that you can prove.
Bibliographical Notes
The three basic isolation levels of transactions were already defined for System R
[Astrahan et al.
1976
], with the highest level (3) meaning repeatable read (i.e.,
serializable in
SQL
parlance). Gray et al. [
1976
] define four isolation levels (degrees
of consistency) for transactions in a transaction model in which a transaction can
declare an update as committed before the transaction terminates. A transaction T
sees degree 0 consistency if it does not overwrite dirty data of other transactions,
degree 1 consistency if in addition it does not commit any writes before termination,
