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1. Function Composition

   Linked via "finite automata"

   Automata Theory and State Machines
   In the study of finite automata and state machines, function composition models the chaining of sequential operations. If a machine transitions from state $qi$ to $qj$ via a function $T1$, and subsequently from $qj$ to $qk$ via $T2$, the combined transition $T2 \circ T1$ represents the net effect of both operations. The set of all possible state transitions under composition forms a Kleene algebra, provided the [empty transition](/entries/e…