Other Models of Reversible Machines

Abstract

Besides reversible Turing machines, various models of reversible machines and automata have been proposed till now. They are reversible finite automata, reversible multi-head finite automata, reversible pushdown automata, reversible counter machines, reversible cellular automata, and others. In this chapter, reversible counter machines (RCMs), and reversible multi-head finite automata (RMFAs) are studied. Reversible cellular automata will be investigated in Chaps. 10–14. A CM is a computing machine that consists of a finite control and a finite number of counters. It is shown that an RCM with only two counters is computationally universal. This result is useful for proving the universality of other reversible systems, since it is a very simple model of computing. On the other hand, an MFA is an acceptor of a language that consists of a finite control, a read-only input tape, and a finite number of input heads. It is proved that any irreversible MFA can be converted into a reversible one with the same number of heads. Hence, the language accepting power of MFAs does not decrease with the constraint of reversibility.