P={P1,P2,P3​,P4} consists of all active processes in an operating system.
R={R1,R2,R3,R4} consists of single instances of distinct types of resources in the system.
The resource allocation graph has the following assignment and claim edges.
Assignment edges: R1→P1,R→P2,R3→P3,R4→P4
Claim edges: P1→R2,P2→R3,P3→R1,P2→R4,P4→R2
Which of the following statement(s) is/are CORRECT?

The correct statements are:
1. Aborting P₂ makes the system deadlock free.
2. Aborting P₁ and P₄ makes the system deadlock free.

Step-by-Step Explanation:

To determine which process abortions will resolve the deadlock, we must identify the cycles present in the Resource Allocation Graph (RAG). A cycle in a resource allocation graph containing single-instance resource types indicates a deadlock state.

1. Identify the Vertices (Processes and Resources):
Processes: $P=\{P_1,P_2,P_3,P_4\}$
Resources (single unit each): $R=\{R_1,R_2,R_3,R_4\}$ (Note: The assignment edge "R→P₂" represents R₂→P₂).

2. Map the Edges in the Graph:
• Assignment Edges (Resource → Process):
R₁ → P₁ (R₁ is held by P₁)
R₂ → P₂ (R₂ is held by P₂)
R₃ → P₃ (R₃ is held by P₃)
R₄ → P₄ (R₄ is held by P₄)

• Claim/Request Edges (Process → Resource):
P₁ → R₂ (P₁ requests R₂)
P₂ → R₃ (P₂ requests R₃)
P₃ → R₁ (P₃ requests R₁)
P₂ → R₄ (P₂ requests R₄)
P₄ → R₂ (P₄ requests R₂)

3. Detect Cycles in the Graph:
By tracing the paths, we find two distinct cycles in the system:
• Cycle 1: P₁ → R₂ → P₂ → R₃ → P₃ → R₁ → P₁
This cycle involves the processes {P₁, P₂, P₃} and resources {R₁, R₂, R₃}.
• Cycle 2: P₂ → R₄ → P₄ → R₂ → P₂
This cycle involves the processes {P₂, P₄} and resources {R₂, R₄}.

4. Analyze the Impact of Aborting Processes:

• Aborting P₂:
Since process P₂ is a participant in both Cycle 1 and Cycle 2, aborting P₂ releases the resources held by P₂ (specifically R₂) and cancels its outstanding requests. This breaks both cycles simultaneously, rendering the system completely deadlock free.

• Aborting P₁ and P₄:
Aborting P₁ alone breaks Cycle 1 but leaves Cycle 2 intact. Aborting P₄ alone breaks Cycle 2 but leaves Cycle 1 intact. However, aborting both P₁ and P₄ breaks both Cycle 1 and Cycle 2, which successfully makes the system deadlock free.

• Other Options:
Aborting P₁ alone or P₃ alone only breaks Cycle 1, leaving Cycle 2 active, so the deadlock would still persist.