Logic of Reversible

Reversible computation is a computation which can be reversed completely: one may run the entire computation backward by inserting the output as new input, thereby obtaining the input one started with. In more formal terms, reversible computation can be characterized by one-to-one operations; i.e., by a reversible, bijective evolution of the computer states onto themselves [Lan61, Ben73, FT82, Ben82, Lan94, LH90]. If only a finite number of such states are involved, this amounts to their permutation. For such a restricted regime, many-to-one operations such as deletion of bits or one-to-many operations such as copying are not allowed. The flow diagram depicted in Fig. 1 was introduced by Landauer [Lan94]. It illustrates differences between one-to-one, many-to-one, and oneto-many information flows. We shall concentrate on a particular class of reversible finite automata which were first discussed in the UMC’98 workshop in Auckland [Svo98b]. Just like irreversible Mealy automata [HU79, Bra84], reversible ones will be characterized by the following properties: