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Consider the following two schedules consisting to two transaction $\mathrm{T}_1$ and $\mathrm{T}_2$ :

Which of the following is/are true about these schedules?

  1. Both $\mathrm{S}_1$ and $\mathrm{S}_2$ are Conflict serializable but not conflict equivalent to each other.
  2. $\mathrm{S}_1$ and $\mathrm{S}_2$ are conflict equivalent but not conflict serializable.
  3. $\mathrm{S}_1$ and $\mathrm{S}_2$ are conflict equivalent and also conflict serializable.
  4. $\mathrm{S}_1$ and $\mathrm{S}_2$ are neither conflict equivalent nor conflict serializable.
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$2$ schedules $\mathrm{S}_1$ and $\mathrm{S}_2$ are conflict equivalent iff Schedule $\mathrm{S}_1$ can be transformed into schedule $\mathrm{S}_1$ by a sequence of non-conflicting swaps of adjacent actions.

The given schedules are conflict equivalent because:

Both are conflict serializable because the precedence graph for $\mathrm{S}_1$ or $\text{S}_2$ will be :

$$\text{T}_1 \longrightarrow $\text{T}_2$

Hence, acyclic.

Another way to check conflict serializability is :

A schedule $\mathrm{S}_1$ is conflict serializable iff The schedule $\mathrm{S}_1$ can be transformed into a serial schedule by a sequence of non-conflicting swaps of adjacent actions.

So, schedules $\text{S}_1 , \text{S}_2$ are conflict-serializable schedules.

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