Aspects of reversibility for classical automata

Abstract

Some aspects of logical reversibility for computing devices with a finite number of discrete internal states are addressed. These devices have a read-only input tape, may be equipped with further resources, and evolve in discrete time. The reversibility of a computation means in essence that every configuration has a unique successor configuration and a unique predecessor configuration. The notion of reversibility is discussed. In which way is the predecessor configuration computed? May we use a universal device? Do we have to use a device of the same type? Or else a device with the same computational power? Do we have to consider all possible configurations as potential predecessors? Or only configurations that are reachable from some initial configurations? We present some selected aspects as gradual reversibility and time-symmetry as well as results on the computational capacity and decidability mainly of finite automata and pushdown automata, and draw attention to the overall picture and some of the main ideas involved.