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MIU-System

An automated solver for Hofstadter’s formal system called MIU.

System Description

The MU puzzle is a puzzle that was made up by Douglas Hofstadter and can be found in his book, Gödel, Escher, Bach. The puzzle uses a simple system called "MIU" to create new strings of symbols.

Characters

M, I, or U

Axiom

The MIU-system only has one axiom: MI.

Rules

Any string resulting from applying these rules on the single axiom or a theorem is a valid theorem. For the following rules x is some valid string of one or more of the character and y is some valid string of zero or more characters.

  1. xI → xIU
  2. MI → Mxx
  3. xIIIy → xUy
  4. xUUy → xy

Program Description

Run the Main class

Press 1 to Generate Theorems from a Provided Theorem

The program takes in a theorem and performs any of the rules that can be applied to it, showing all possible theorems that can be derived in a single step. This does not validate the input theorem, so the results asre only valid if the input theorem is valid, but will be produced regardless.

What would you like to do:
1. Generate Theorems (Only Valid if the initial theorem is valid)
2. Validate Theorem
3. Exit
Choice: 1

Enter a MIU theorem: MIUUUUIIIU
Applying rule 2: MIUUUUIIIUIUUUUIIIU
Applying rule 3: MIUUUUUU 
Applying rule 4: MIUUIIIU 
New Theorems: [MIUUIIIU, MIUUUUIIIUIUUUUIIIU, MIUUUUUU]

What would you like to do:
1. Generate Theorems (Only Valid if the initial theorem is valid)
2. Validate Theorem
3. Exit
Choice: 1

Enter a MIU theorem: MIUIIUIIIIUUUIIUUI
Applying rule 1: MIUIIUIIIIUUUIIUUIU
Applying rule 2: MIUIIUIIIIUUUIIUUIIUIIUIIIIUUUIIUUI
Applying rule 3: MIUIIUIUUUUIIUUI MIUIIUUIUUUIIUUI 
Applying rule 4: MIUIIUIIIIUIIUUI MIUIIUIIIIUUUIII 
New Theorems: [MIUIIUIIIIUIIUUI, MIUIIUIIIIUUUIII, MIUIIUIIIIUUUIIUUIIUIIUIIIIUUUIIUUI, MIUIIUIIIIUUUIIUUIU, MIUIIUIUUUUIIUUI, MIUIIUUIUUUIIUUI]

Press 2 to Validate a Provided Theorem

The program takes in a desired theorem to be proven and the maximum number of steps to be performed on the axiom MI to find the provided theorem.

What would you like to do:
1. Generate Theorems (Only Valid if the initial theorem is valid)
2. Validate Theorem
3. Exit
Choice: 2

Enter a MIU theorem: MIUUI
Enter a number of steps: 5
The theorem is valid.

What would you like to do:
1. Generate Theorems (Only Valid if the initial theorem is valid)
2. Validate Theorem
3. Exit
Choice: 2

Enter a MIU theorem: MUIIIUUIU
Enter a number of steps: 6
The theorem could not be confirmed as valid.

Press 3 to Exit