Making Universal Reversible Turing Machines
نویسنده
چکیده
Studies on universal Turing machines (UTM) have a long history, and various small UTMs have been given till now [2, 3, 10–12]. Here, we investigate the problem of constructing small UTMs under the constraint of reversibility, which is a property closely related to physical reversibility. Let URTM(m,n) denote an m-state n-symbol universal reversible Turing machine. So far, six kinds of small URTMs have been shown. They are URTM(10,8), URTM(13,7), URTM(15,6), URTM(17,5), URTM(24,4), and URTM(32,3) given in [4, 7–9]. All of them can simulate cyclic tag systems, which are universal string rewriting systems proposed by Cook [1]. Furthermore, by the methods of reducing the number of states or symbols [5, 7], URTM(3,36654), URTM(4,168), and URTM(138,2) are obtained, though their sizes are large. The reference [6] contains computer simulation results, and the description files of the URTMs. In this talk, we give a survey on these URTMs, and explain how they are designed. We also discuss open problems on URTMs.
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