Universal Computer

A universal Turing machine simulator in Python. Demonstrates the foundational concept of computability: a single machine that can simulate any other Turing machine.

How It Works

A Turing machine has a tape (infinite in both directions), a read/write head, a set of states, and a transition function. Given a state and the symbol under the head, the machine writes a new symbol, moves left/right/stay, and transitions to a new state. It halts when it reaches the halt state.

This implementation uses:

• Dictionary-based tape -- positions map to symbols, missing positions are blank
• JSON machine descriptions -- portable, human-readable definitions
• Configurable step limit -- prevents infinite loops

Usage

# Increment binary number: 1101 (13) -> 1110 (14)
python3 utm.py machines/incrementer.json --tape "1101"

# Check parity
python3 utm.py machines/even_odd.json --tape "1111"

Included Machines

Machine	File	Description
Binary Incrementer	incrementer.json	Adds 1 to a binary number
Even/Odd	even_odd.json	Determines parity of a unary number

Creating Your Own Machine

{
  "states": ["q0", "q1", "halt"],
  "alphabet": ["0", "1"],
  "blank": "_",
  "transitions": {
    "q0:0": ["q0", "0", "R"],
    "q0:1": ["q1", "1", "R"],
    "q0:_": ["halt", "_", "S"]
  },
  "start": "q0",
  "halt": "halt"
}

Each transition key is "state:symbol" mapping to [next_state, write_symbol, direction] where direction is L (left), R (right), or S (stay).

Development

pip install pytest
pytest tests/ -v

Theory

Alan Turing proved in 1936 that a universal Turing machine can compute anything that any Turing machine can compute. Every computer is a physical realization of this idea.

License

Proprietary -- BlackRoad OS, Inc.