What makes up a finite state machine discrete math?
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Finite State Machines
A finite state machine (sometimes called a finite state automaton) is a computation model that can be implemented with hardware or software and can be used to simulate sequential logic and some computer programs. Finite state automata generate regular languages. Finite state machines can be used to model problems in many fields including mathematics, artificial intelligence, games, and linguistics.
A system where particular inputs cause particular changes in state can be represented using finite state machines. This example describes the various states of a turnstile. Inserting a coin into a turnstile will unlock it, and after the turnstile has been pushed, it locks again. Inserting a coin into an unlocked turnstile, or pushing against a locked turnstile will not change its state