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---
license: mit
tags:
- formal-verification
- coq
- threshold-logic
- neuromorphic
- majority
---
# tiny-Majority-verified
Formally verified majority gate for 8-bit inputs. Single threshold neuron computing majority function with 100% accuracy.
## Architecture
| Component | Value |
|-----------|-------|
| Inputs | 8 |
| Outputs | 1 |
| Neurons | 1 |
| Parameters | 9 |
| Weights | [1, 1, 1, 1, 1, 1, 1, 1] |
| Bias | -5 |
| Activation | Heaviside step |
## Key Properties
- 100% accuracy (256/256 inputs correct)
- Coq-proven correctness
- Single threshold neuron
- Integer weights
- Fires when ≥5 of 8 inputs are true
- Equivalent to 5-out-of-8 threshold
## Usage
```python
import torch
from safetensors.torch import load_file
weights = load_file('majority.safetensors')
def majority_gate(bits):
# bits: list of 8 binary values
inputs = torch.tensor([float(b) for b in bits])
weighted_sum = (inputs * weights['weight']).sum() + weights['bias']
return int(weighted_sum >= 0)
# Test
print(majority_gate([0,0,0,0,0,0,0,0])) # 0 (no majority)
print(majority_gate([1,1,1,1,0,0,0,0])) # 0 (4/8, not majority)
print(majority_gate([1,1,1,1,1,0,0,0])) # 1 (5/8, majority!)
print(majority_gate([1,1,1,1,1,1,1,1])) # 1 (8/8, majority)
```
## Verification
**Coq Theorem**:
```coq
Theorem majority_correct : forall x0 x1 x2 x3 x4 x5 x6 x7,
majority_circuit [x0; x1; x2; x3; x4; x5; x6; x7] =
majority_spec [x0; x1; x2; x3; x4; x5; x6; x7].
```
Proven axiom-free via three methods:
1. **Exhaustive**: Verified on all 256 inputs
2. **Universal**: Quantified proof over all boolean combinations
3. **Algebraic**: Characterized via hamming weight ≥ 5
**Algebraic characterization**:
```coq
Theorem majority_hamming_weight (xs : list bool) :
length xs = 8 ->
majority_circuit xs = true <-> hamming_weight xs >= 5.
```
Full proof: [coq-circuits/Threshold/Majority.v](https://github.com/CharlesCNorton/coq-circuits/blob/main/coq/Threshold/Majority.v)
## Circuit Operation
Input with k true bits produces weighted sum: k*1 - 5 = k - 5
- k < 5: weighted_sum < 0 → output 0 (no majority)
- k ≥ 5: weighted_sum ≥ 0 → output 1 (majority)
## Applications
- Voting systems
- Fault-tolerant computing
- Consensus protocols
- Error correction (majority voting)
## Citation
```bibtex
@software{tiny_majority_prover_2025,
title={tiny-Majority-verified: Formally Verified Majority Gate},
author={Norton, Charles},
url={https://huggingface.co/phanerozoic/tiny-Majority-verified},
year={2025}
}
```
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