A small minimal aperiodic reversible Turing machine

Reversible Turing machines with a small number of states

Some improvements in fuzzy turing machines

In this paper, we improve some previous definitions of fuzzy-type Turing machines to obtain degrees of accepting and rejecting in a computational manner. We apply a BFS-based search method and some level’s upper bounds to propose a computational process in calculating degrees of accepting and rejecting. Next, we introduce the class of Extended Fuzzy Turing Machines equipped with indeterminacy s...

Time/Space Trade-Offs for Reversible Computation

A reversible Turing machine is one whose transition function is 1, so that no instantaneous description (ID) has more than one predecessor. Using a pebbling argument, this paper shows that, for any e > 0, ordinary multitape Turing machines using time T and space S can be simulated by reversible ones using time O(T +) and space O(S log T) or in linear time and space O(ST). The former result impl...

Making Universal Reversible Turing Machines

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 URT...

The Smallest Arithmetic Logic Unit

There have been many designs for „small universal computers“. The Turing machine (1936), for example, remains unsurpassed: it consists only of memory, and a small processor with a few number of internal states. The memory can be designed to store only binary digits (0 and 1) and the number of states can be minimized. Scheming minimal universal Turing machines has been a mental sport for years [1].