Abstract
The closure properties of the class of languages defined by real-time, online, multi-tape Turing machines are proved. The results obtained are, for the most part, negative and, as one would expect, asymmetric. It is shown that the results remain valid for a broad class of real-time devices. Finally, the position of the class of real-time definable languages in the 舠classical舡 linguistic hierarchy is established. © 1967, ACM. All rights reserved.