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Introduction
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Coarse graining Alice and Dinah
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Coarse graining part I - Clustering algorithms
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Coarse graining part II - Entropy
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Markov Chains
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Mathematics of coarse grained Markov chains
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Mathematics of Coarse grained Markov Chains: The General Case
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A puzzle: origin of the slippy counter
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Where we are so far
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Cellular Automata: Introduction
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Israeli and Goldenfeld; projection and commuting diagrams
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Networks of Renormalization
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Fixing a projection: From CA’s to Ising
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Introduction to the Ising Model
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Coarse-graining the Lattice
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Inducing Quartets & Commutation Failure
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Finding Fixed Points
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Ising Model Simulations
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Poking the Creature: An Introduction to Group Theory
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Irreversible Computations, Forgetful Computers and the Krohn-Rhodes Theorem
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From Quantum Electrodynamics to Plasma Physics
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The Thermal Physics of Plasma
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How does a particle move the plasma?
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Charge Renormalization and Feedback
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Conclusion: Keeping the things that matter
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5.2 Irreversible Computations, Forgetful Computers and the Krohn-Rhodes Theorem » Quiz Solution
What is a semi-group?
A. a subset of a group's moves (of the things you can do to a normal creature)
B. a creature where some of the moves can not be universally "undone"
C. a creature with a move that takes it invariably to a unique internal state regardless of current state.
D. (B), with (C) as a special case.
Answer (D). A creature of type (C) has a reset move built in; but creatures like (B) are the more general case of systems with irreversible operations. These are called semi-groups. The Krohn-Rhodes theorem tells you that all creatures of type (B) have, in their hierarchical decomposition, a "reset" machine of like (C).