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In automata theory and control theory, branches of mathematics, theoretical computer science and systems engineering, a noncommutative signal-flow graph is a tool for modeling interconnected systems and state machines by mapping the edges of a directed graph to a ring or semiring.
A single edge weight might represent an array of impulse responses of a complex system , or a character from an alphabet picked off the input tape of a finite automaton, while the graph might represent the flow of information or state transitions.
As diverse as these applications are, they share much of the same underlying theory.
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