A deterministic two-way multi-head finite automaton can be converted into a reversible one with the same number of heads

Abstract

A two-way multi-head finite automaton (MFA) is a variant of a finite automaton consisting of a finite-state control, a finite number of heads that can move in two directions, and a read-only input tape. Here, we show that for any given deterministic MFA we can construct a reversible MFA with the same number of heads that accepts the same language as the former. We then apply this conversion method to a Turing machine. By this, we can obtain, in a simple way, an equivalent reversible Turing machine that is garbage-less, uses the same number of tape symbols, and uses the same amount of the storage tape. © 2013 Springer-Verlag Berlin Heidelberg.