Looking at Wikipedia, what I'm thinking of may be equivalent to a Linear Bounded Automaton. https://en.wikipedia.org/wiki/Linear_bounded_automaton https://en.w

Looking at Wikipedia, what I'm thinking of may be equivalent to a Linear Bounded Automaton. https://en.wikipedia.org/wiki/Linear_bounded_automaton https://en.wikipedia.org/wiki/Linear_bounded_automaton Specifically, I'm thinking of the "less restrictive definition." Also, I realize I elided over the fact that a FSM traditionally reads its input "as it goes", whereas a TM has its input pre-written to the tape. To work the way the TM would, my FSM would need to have its initial state set to the one corresponding to the TM initial configuration, and it would take some clock input that it would ignore at each step. Each state would have one transition that would ultimately lead to a terminal state, if it doesn't loop forever. Actually constructing an FSM based on this idea is impractical because constructing it would require a huge number of states. Again, the number of FSM states would be equal to (# TM states) * (number of cell positions) * (# symbols)^(bounds of tape). For anything non-trivial that's a ludicrous number of states. Similarly, constructing the state transition table would be O((# symbols)^(bounds of tape)) operations. Logically, it can be done but it's only useful as a mental exercise.