Do circular tapes exist in Turing Machines?

Question

I've been looking for information about this topic without success. Have someone described Turing Machines over circular tapes instead lineal and infinite? Like the tape could be described with modular arithmetics. If so (which I find very probable), who are the authors/papers I should read?

Thank you and sorry if the question is too elementary or naive.

Answer 1

Yes. These machines have been studied under the name of clockwise Turing machines by Neary and Woods [3], who proved that

Turing machine → clockwise Turing machine → cyclic tag system → Rule 110

Neary also indicates that these machines are closed to Kudlek and Rogozhin’s [1, 2] Post machines.

[1] M. Kudlek and Y. Rogozhin, New small universal circular Post machines. In Rusins Freivalds, editor, Fundamentals of Computation Theory (FCT), volume 2138 of LNCS, pages 217–227, Riga, Latvia, August 2001. Springer.

[2] M. Kudlek and Y. Rogozhin, Small universal circular Post machines. Computer Science Journal of Moldova, 9(1):34–52, 2001.

[1] T. Neary and D. Woods, P-completeness of cellular automaton Rule 110, Automata, languages and programming. Part I, 132--143, LNCS 4051, Springer, Berlin, 2006.