The namesake of these things determined that asking if they halt is undecidable.
Mark Burgin discussed "inductive" types of these things in an article that treats their process of generating "words" as closely resembling the task of calculating a real number to a desired precision. The Kolmogorov complexity of an input is formally defined as the simplest number of states used to encode that input in these models, which are formally defined with a 7-tuple. Treating these things as black boxes, or (*)  "oracles", is often done in proofs that make use of polynomial-time reductions. The namesake of these things determined that asking if they halt is undecidable. A head that reads and writes bits on an infinite tape is one component of, for 10 points, what entities that closely model computers, and which are named for a British computer scientist?
Mark Burgin discussed "inductive" types of these things in an article that treats their process of generating "words" as closely resembling the task of calculating a real number to a desired precision.
Turing machine s [prompt on  machine s or  abstract machine s or  abstract computer s] 