The transition function is a fundamental concept in automata theory that defines how a state machine changes states based on input symbols. It is crucial for understanding the behavior of both deterministic and nondeterministic finite automata, as it dictates the next state for each possible input and current state combination. This function plays a vital role in the minimization of finite automata, establishes equivalences between different computational models, and aids in analyzing the capabilities of more complex computational systems like Turing machines and cellular automata.
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