Universal Reversible Turing Machines
In this chapter, the problem of finding small universal Turing machines (UTMs) that satisfy the reversibility condition is studied. Such UTMs are called universal reversible Turing machines (URTMs). Let URTM(m,n) denote an m-state n-symbol URTM.We give several URTM(m,n)’s with small m and n. Here, a method of simulating cyclic tag systems (CTSs) by URTMs is employed. A CTS is a kind of a very simple string rewriting system, and is known to be computationally universal. By this method, URTM(10,8), URTM(13,7), URTM(15,6), URTM(17,5), URTM(24,4), and URTM(32,3) are obtained. On the other hand, it is generally difficult to design small reversible TMs with two symbols or with a very small number of states. For these cases, we apply general conversion methods to some of the above small URTMs, and obtain URTM(138,2), URTM(4,168), and URTM(3, 36654).
Keywordsuniversal reversible Turing machine small universal Turing machine cyclic tag system
Unable to display preview. Download preview PDF.