# Standard Operating Procedure
**Document Number:** MUTEX-SYS-001  
**Standard Operating Procedure (SOP):** Mutual Exclusion Protocol for Two-Process Coordination  
**Revision:** 1.0  
**Last Updated:** [DATE]

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## Contents

1. Introduction  
    1.1 Purpose  
    1.2 System Overview  
    1.3 Regulatory Compliance  

2. System Specifications  
    2.1 Parameters and State Variables  
    2.2 Mutual Exclusion Configuration  

3. Operational Protocols  
    3.1 Startup Behavior  
    3.2 Request and Entry into Critical Section  
    3.3 Turn-Based Conflict Resolution  

4. Emergency Operations  
    4.1 Deadlock Detection  
    4.2 State Recovery Process  

5. Maintenance Requirements  
    5.1 Process Integrity Checks  
    5.2 Turn Variable Diagnostics  

6. Quality Assurance  
    6.1 Liveness Verification  
    6.2 Mutual Exclusion Invariants  

7. Security Protocols  
    7.1 Access Control for Shared Resources  
    7.2 Process Isolation  

8. Environmental Considerations  
    8.1 Time Determinism Under Load  
    8.2 Fault Tolerance in Shared Memory  

9. Training Requirements  
    9.1 Protocol Interpretation  
    9.2 State Transition Analysis  

10. Document Control  
    10.1 Revision History  
    10.2 Authorization  

11. Process Flows and State Transitions  
    11.1 State Transition Logic  
    11.2 Conflict Resolution Sequence  
    11.3 Fairness and Starvation Avoidance  

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## 1. Introduction

### 1.1 Purpose
- Establish a reliable mutual exclusion protocol for two concurrent processes.
- Prevent simultaneous entry into the critical section to maintain data integrity.

### 1.2 System Overview
- The system contains two processes (`P1` and `P2`) managing shared access.
- Each process transitions through three logical states:  
  - `n` (non-critical), `t` (trying), `c` (critical).
- Access is coordinated using a shared `turn` variable indicating priority.

### 1.3 Regulatory Compliance
- Aligned with formal safety and liveness verification protocols.
- Ensures conformance to synchronization requirements in embedded and concurrent systems.

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## 2. System Specifications

### 2.1 Parameters and State Variables
- `state1` and `state2`: Current state of Process 1 and Process 2 respectively.
- Valid states:  
  - `n1/n2`: Non-critical section  
  - `t1/t2`: Trying to enter critical section  
  - `c1/c2`: Inside critical section
- `turn`: Shared variable set to 1 or 2, indicating which process should yield.

### 2.2 Mutual Exclusion Configuration
- Both processes cannot be in `c1` and `c2` simultaneously.
- Entry to the critical section is determined based on:
  - State of the other process.
  - Current value of the `turn` variable.

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## 3. Operational Protocols

### 3.1 Startup Behavior
- Initialize both processes to the non-critical section:
  - `state1 = n1`, `state2 = n2`.
- Set `turn = 1` (default starting priority to Process 1).

### 3.2 Request and Entry into Critical Section
- Transition from `n → t` (request phase) occurs when the other process is not in critical section.
- Transition from `t → c` (entry to critical section) is permitted if:
  - The other process is in `n` (non-critical), or
  - Both are trying and `turn` favors the current process.

### 3.3 Turn-Based Conflict Resolution
- After completing its critical section, a process transitions back to `n` and updates the `turn`:
  - If P1 finishes and P2 is waiting, `turn := 2`.
  - If P2 finishes and P1 is waiting, `turn := 1`.

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## 4. Emergency Operations

### 4.1 Deadlock Detection
- Check if both processes are stuck in trying (`t1`, `t2`) without progressing to `c1` or `c2`.
- Trigger alert if fairness or transition liveness is violated.

### 4.2 State Recovery Process
- Reset `state1`, `state2`, and `turn` if deadlock or illegal state is detected.
- Ensure mutual exclusion is re-established before resuming operations.

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## 5. Maintenance Requirements

### 5.1 Process Integrity Checks
- Periodically verify that each process transitions through legal states only.
- Confirm state reset mechanisms are functional after each cycle.

### 5.2 Turn Variable Diagnostics
- Monitor consistency and fairness of `turn` updates.
- Ensure the `turn` alternates as expected to avoid process starvation.

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## 6. Quality Assurance

### 6.1 Liveness Verification
- Confirm that if `state1 = t1`, then eventually `state1 = c1`.
- Confirm that if `state2 = t2`, then eventually `state2 = c2`.

### 6.2 Mutual Exclusion Invariants
- Assert that `state1 = c1` and `state2 = c2` never occur simultaneously.
- Use model checkers to verify safety (invariants) and liveness (eventualities).

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## 7. Security Protocols

### 7.1 Access Control for Shared Resources
- Ensure mutual exclusion is preserved during concurrent operations.
- Only one process allowed in critical section at a time.

### 7.2 Process Isolation
- Maintain local state per process.
- Prevent unauthorized state changes via unguarded transitions.

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## 8. Environmental Considerations

### 8.1 Time Determinism Under Load
- Ensure state transitions occur without delay under high load.
- Avoid long waits due to missed fairness windows.

### 8.2 Fault Tolerance in Shared Memory
- Validate correctness of `turn` updates in memory-constrained or noisy environments.
- Add parity or checksum checks to shared variable communication.

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## 9. Training Requirements

### 9.1 Protocol Interpretation
- Train operators on states `n`, `t`, and `c` and their meanings.
- Understand the role of `turn` in preventing simultaneous access.

### 9.2 State Transition Analysis
- Practice tracing execution under normal and edge-case scenarios.
- Use visualization tools to follow the ring of state changes.

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## 10. Document Control

### 10.1 Revision History
- Rev 1.0 – Initial SOP derived from formal mutex model (mutex.txt)

### 10.2 Authorization
- Approved by: Embedded Systems Architect  
- Reviewed by: Safety Verification Team

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## 11. Process Flows and State Transitions

### 11.1 State Transition Logic

**For Process 1:**
- `n1 → t1` if state2 in (`n2`, `t2`, `c2`)  
- `t1 → c1` if state2 is `n2`, or (`t2` and `turn = 1`)  
- `c1 → n1` (after exiting critical section)

**For Process 2:**
- `n2 → t2` if state1 in (`n1`, `t1`, `c1`)  
- `t2 → c2` if state1 is `n1`, or (`t1` and `turn = 2`)  
- `c2 → n2` (after exiting critical section)

### 11.2 Conflict Resolution Sequence
- Processes resolve conflict using the `turn` variable:
  - Only one will enter the critical section when both are in `t`.

### 11.3 Fairness and Starvation Avoidance
- Use `turn` toggling logic to ensure neither process is starved.
- Each trying state is guaranteed eventual access (fair scheduling).