Transactions

Sequence of indivisible DML requests

Atomicity
Consistency
Isolation
Durability

Subsystems

Concurrency Control Management
- Responsible for scheduling the execution of reads and writes on physical objects in a way that ensures transaction isolation
Recovery Management
- Responsible for enduring transaction atomicity and durability

DML processing is responsible for ensuring the part of the transaction consistency defined by the integrity constraints

Database is a finite set of independent physical objects $x_{j}$ that are read and written to transactions $T_{i}$

$r_{i} [x_{j}]$ - Transaction $T_{i}$ reads object $x_{j}$
$w_{i} [x_{j}]$ - Transaction $T_{i}$ writes object $x_{j}$

Transactions

$T_{i}$ is a sequence of read and write operations on a database
$T_{i} = r_{i} [x_{1}], r_{i} [x_{2}], w_{i} [x_{1}], \dots, r_{i} [x_{4}], w_{i} [x_{2}], c_{i}$