Space-Bounded Reversible Turing Machines

Abstract

In this chapter, we investigate the problem how reversibility and determinism affect language accepting capability of space-bounded Turing machines (TM). A space-bounded TM is a model whose memory space is bounded by a space function S(n), where n is the input length. Here, we study the relationship among four classes of space-bounded TMs, i.e., irreversible nondeterministic (IN), irreversible deterministic (ID), reversible nondeterministic (RN), and reversible deterministic (RD) ones.We first show a very simple method of simulating an IDTM by an RDTM that uses the same numbers of storage tape symbols and storage tape squares. By a similar method, we also show that an RNTM that satisfies some condition can be simulated by an RDTM that uses the same numbers of storage tape symbols and storage tape squares. Therefore, IDTMs, RNTMs, and RDTMs with the same space function are equivalent in their language accepting powers, and thus an RDTM has relatively high capability in spite of the constraints of reversibility and determinism.