Abstract
An off-line machine is a Turing machine with a separate read-only input tape. Such a machine is said to have a ‘Brownian’ input head if it has no control over and cannot observe the moves of the read-only head scanning the input tape. It is shown in this note that the binary languages (i.e., languages over a two-symbol alphabet) recognized by such machines are all regular. The proof is not constructive and relies heavily on the so-called ‘finite sequences theorem’ in the theory of well-partial-ordering.
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