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 # Conflict Serialisability
+
 If a concurrent schedule organises conflicting operations in the same way as a serial schedule, the results are the same.
 This is called conflict serialisability, which can be tested using precedence graphs.

 ## Directed Graph
+
 - ![](Pasted%20image%2020240213131718.png)
 - ![](Pasted%20image%2020240213131802.png)
 - ![](Pasted%20image%2020240213131815.png)
+
 # Precedence Graph

+- Used to determine if a schedule is serialisable.
+- It is serialisable if the graph has no cycles.
+
+## Example Using Serial Schedule
+
+- ![](Pasted%20image%2020240213132227.png)
+- This schedule is serialisable because the graph is acyclic. ex. No directed cycle.
+
+## Example Using Non-Serial Schedule
+
+- ![](Pasted%20image%2020240213132603.png)
+- This schedule is serialisable due to being acyclic.
+- It is equivalent due to
+	- T2 reading the written value of X from T1
+	- T1 reading the value of X from the database
+	- T1 is the last transaction to write Y
+	- T2 is the last transaction to write X
+
+## Example Using Non-Serialisable Schedule
+
+- ![](Pasted%20image%2020240213133455.png)
+- This schedule is non-serialisable since the graph is cyclic.
+
+## Example 4
+
+- ![](Pasted%20image%2020240213161136.png)
+- Cyclic graph, non serialisable.
+
+# Tutorial Questions: Chapter 28
+
+1. What is a serial schedule?
+A serial schedule is an order of operations where each is complete before a new operation starts. Ex. No interleaves operations.
+2. Why is a serial schedule considered correct?
+Each operation is either successful or aborted before a new operation starts, meaning every operation is correct and the database is consistent.
+3. What is a serialisable schedule?
+A serialisable schedule is a concurrent schedule with an acyclic precedence graph. The operation is the same as a serial schedule.
+4. Why is a serialisable schedule considered correct?
+Since the operation is functionally the same as a serial schedule, we can consider it correct.
+
+5. The precedence graph is serialisable since it is acyclic. No directed cycles.
+6. T1.1 -> T2.2, T1.2 -> T2.1, T1.2 -> T2.2, T1.2 -> T3.1, T2.2 -> T3.1
+- ![](Pasted%20image%2020240213172304.png)
+The graph is serialisable since there are no directed cycles.
+
+1. T2.1 -> T1.1, T1.1 -> T2.2, T2.2 -> T1.2
+- ![](Pasted%20image%2020240213172509.png)
+The graph is not serialisable since there is a directed cycle
+
+1. T1.1 -> T2.1, T1.2 -> T2.1
+- ![](Pasted%20image%2020240213172702.png)
+The graph is serialisable since there are no directed cycles.
+
+1. T1.1 -> T2.2, T2.1 -> T1.2, T1.2 -> T2.2
+- ![](Pasted%20image%2020240213172509.png)
+The graph is not serialisable since there are directed cycles