Computational Mechanics:Mathematical Foundations

• Casual state = Condition of knowledge about future

• _-Machines = {Causal states, Transitions}

• Optimality Theorem:

  _-Machines are optimal predictors of environment.
  

• Minimality Theorem:

  Of the optimal predictors, _-Machines are smallest.
  

• Uniqueness Theorem:

  Up to isomorphism, an _-Machine is unique.
  

• The Point:

  Discovering an _-Machine is the goal for any learning process. Practicalities may preclude this, but this is the goal.
  
  (w/ DP Feldman/CR Shalizi)

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