# Standard Operating Procedure
**Document Number:** RING-SYS-001  
**Standard Operating Procedure (SOP):** Ring Oscillator Logic System  
**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 Logical Parameters and Variables  
    2.2 Hardware Configuration  

3. Operational Protocols  
    3.1 Initialization Sequence  
    3.2 Ring Oscillation Cycle  
    3.3 Inverter Behavior  

4. Emergency Operations  
    4.1 Oscillation Fault Detection  
    4.2 Fail-Safe Logic Response  

5. Maintenance Requirements  
    5.1 Signal Integrity Checks  
    5.2 Gate Recalibration  

6. Quality Assurance  
    6.1 Logical Invariance Verification  
    6.2 Liveness Property Conformance  

7. Security Protocols  
    7.1 State Stability Enforcement  
    7.2 Redundancy and Verification  

8. Environmental Considerations  
    8.1 Electrical Noise Handling  
    8.2 Temperature Stability  

9. Training Requirements  
    9.1 System Behavior Interpretation  
    9.2 Model Checking Tools Familiarity  

10. Document Control  
    10.1 Revision History  
    10.2 Authorization  

11. Process Flows and State Transitions  
    11.1 Inverter State Transitions  
    11.2 Oscillation Feedback Loop  
    11.3 Fairness and Liveness Conditions  

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## 1. Introduction

### 1.1 Purpose
- Define safe and predictable behavior for a 3-inverter ring oscillator system.
- Provide operational guidance and verification protocols for oscillation logic.

### 1.2 System Overview
- Comprises three logic inverters connected in a closed loop.
- Output of each inverter is the input to the next, creating continuous inversion.
- System exhibits oscillatory behavior based on logical negation across the ring.

### 1.3 Regulatory Compliance
- Compliant with formal verification principles for liveness and safety.
- Aligned with logical modeling practices for real-time embedded systems.

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## 2. System Specifications

### 2.1 Logical Parameters and Variables
- `output`: Boolean value indicating logical HIGH (`TRUE`) or LOW (`FALSE`).
- `input`: Signal received from previous inverter in the ring.
- Initial state: `FALSE` for all outputs.
- Transition logic: `next(output) := !input`.

### 2.2 Hardware Configuration
- Three inverter modules: gate1, gate2, gate3.
- Connectivity:
  - gate1.input ← gate3.output
  - gate2.input ← gate1.output
  - gate3.input ← gate2.output

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## 3. Operational Protocols

### 3.1 Initialization Sequence
- On startup, all inverter outputs are initialized to `FALSE`.
- State machine transitions begin immediately via logical negation.
- Fair scheduling assumed for each module (`FAIRNESS running`).

### 3.2 Ring Oscillation Cycle
- The three inverters alternate states in sequence:
  - gate1 → gate2 → gate3 → gate1 ...
- Oscillation relies on asynchronous signal transitions and inversion.
- No external clock is required; behavior is self-timed.

### 3.3 Inverter Behavior
- Each inverter updates its output based on the inverse of its input.
- Outputs toggle as the system progresses through its ring cycle.
- Ensures continuous state change as long as the process is fair.

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## 4. Emergency Operations

### 4.1 Oscillation Fault Detection
- Monitor for frozen state (no toggling over time).
- If `AG AF gate1.output` or `AG AF !gate1.output` fails, raise fault alert.

### 4.2 Fail-Safe Logic Response
- Halt oscillation propagation if one inverter becomes unresponsive.
- Reset output values or trigger manual reinitialization.

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## 5. Maintenance Requirements

### 5.1 Signal Integrity Checks
- Verify each inverter receives valid input from preceding gate.
- Check for transient faults that may introduce static loops.

### 5.2 Gate Recalibration
- Inspect inverter thresholds periodically.
- Replace components showing drift in logical thresholds or toggling failure.

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## 6. Quality Assurance

### 6.1 Logical Invariance Verification
- Ensure that the output of any gate will eventually toggle:
  - `AG AF gate1.output` and `AG AF !gate1.output` hold true.

### 6.2 Liveness Property Conformance
- Confirm that the system does not settle into a stable state.
- Use model checkers to verify alternating truth values over infinite runs.

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## 7. Security Protocols

### 7.1 State Stability Enforcement
- Guard against indefinite holding of a single logical value.
- Introduce watchdog logic if necessary to ensure toggling.

### 7.2 Redundancy and Verification
- Redundant gates may be added for error detection.
- Simulation and formal verification tools must confirm correct transitions.

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## 8. Environmental Considerations

### 8.1 Electrical Noise Handling
- Include debouncing or filtering for voltage fluctuations.
- Shield wiring between gates in physical implementations.

### 8.2 Temperature Stability
- Validate inverter thresholds across temperature ranges.
- Incorporate temperature-compensated logic if needed.

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## 9. Training Requirements

### 9.1 System Behavior Interpretation
- Operators must understand ring oscillator behavior and state toggling.
- Training on interpreting logical waveforms over time.

### 9.2 Model Checking Tools Familiarity
- Team must be trained on using formal verification tools (e.g., NuSMV).
- Interpret results of safety (`AG`) and liveness (`AF`) specifications.

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## 10. Document Control

### 10.1 Revision History
- Rev 1.0 – Initial SOP derived from formal ring oscillator specification (ring.txt)

### 10.2 Authorization
- Approved by: Hardware Logic Design Lead  
- Reviewed by: Verification and Validation Team

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## 11. Process Flows and State Transitions

### 11.1 Inverter State Transitions
- State at time `t+1`: output = NOT(input)
- Inputs are derived from the output of the previous inverter in the ring.

### 11.2 Oscillation Feedback Loop
- gate1.output → gate2.input  
- gate2.output → gate3.input  
- gate3.output → gate1.input  
- Loop ensures feedback and propagation of toggling behavior.

### 11.3 Fairness and Liveness Conditions
- The `FAIRNESS running` constraint ensures each inverter will execute.
- Liveness properties:
  - Eventually gate1 will be `TRUE`
  - Eventually gate1 will be `FALSE`