Invariant Principle

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The Invariant Principle is applicable to algorithms (games, transformations). Some task is repeatedly performed. What stays the same? What remains invariant? Here is a saying easy to remember:

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The Invariant Principle is applicable to algorithms (games, transformations). Some task is repeatedly performed. What stays the same? What remains invariant? Here is a saying easy to remember: If there is repetition, look for what does not change! In algorithms there is a starting state S and a sequence of legal steps (moves, transformations).

One looks for answers to the following questions:

  1. Can a given end state be reached?2. Find all reachable end states.3. Is there convergence to an end state?4. Find all periods with or without tails, if any.