# Reversible space equals deterministic space

@article{Lange1997ReversibleSE, title={Reversible space equals deterministic space}, author={Klaus-J{\"o}rn Lange and P. McKenzie and A. Tapp}, journal={Proceedings of Computational Complexity. Twelfth Annual IEEE Conference}, year={1997}, pages={45-50} }

This paper describes the simulation of an S(n) space-bounded deterministic Turing machine by a reversible Turing machine operating in space S(n). It thus answers a question posed by C. Bennett (1989) and refutes the conjecture, made by M. Li and P. Vitanyi (1996), that any reversible simulation of an irreversible computation must obey Bennett's reversible pebble game rules.

#### Topics from this paper

#### 45 Citations

Language Recognition by Reversible Partitioned Cellular Automata

- Computer Science
- Automata
- 2014

It is proved RPCAs are also equivalent toDLBAs by showing a construction method of an RPCA that simulates a given DLBA, and the reversibility constraint does not decrease the ability of PCAs. Expand

Reversible languages having finitely many reduced automata

- Computer Science
- AFL
- 2017

A forbidden pattern is given capturing the reversible regular languages having only finitely many reduced reversible automata, allowing an efficient (NL) decision procedure. Expand

Relationships between quantum and classical space-bounded complexity classes

- Mathematics, Computer Science
- Proceedings. Thirteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat. No.98CB36247)
- 1998

It follows that unbounded error, space O(s) bounded quantum Turing machines and probabilistic Turing machines are equivalent in power, which implies that any space s QTM can be simulated deterministically in space O (s/sup 2/), and further that any (unbounded-error) QTM running in log-space can be simulation in NC/Sup 2/. Expand

Quantum versus Deterministic Counter Automata

- Mathematics, Computer Science
- COCOON
- 2002

It is proved that under some practically reasonable assumption, quantum ones are strictly stronger than deterministic ones in two-way one-counter automata, and for any fixed k, quantum Ones and deterministic Ones are incomparable in one-way k- counter automata. Expand

2 Previous Work on Linear-time Simulations

- 2015

Bennett has shown how to simulate arbitrary forwards-only computations by fully reversible computation. In particular he has given a space-efficient linear time simulation. After describing a… Expand

Relativized Separation of Reversible and Irreversible Space-Time Complexity Classes

- Mathematics, Computer Science
- ArXiv
- 2017

This work provides an oracle-relativized proof of the separation, and of a lower bound on space for linear-time reversible simulations, of a problem for which Bennett's algorithm is optimal. Expand

Concise Representations of Reversible Automata 3 2 Preliminaries

- 2017

We present two concise representations of reversible automata. Both representations have a size which is comparable with the size of the minimum equivalent deterministic automaton and can be… Expand

Quantum simulations of classical random walks and undirected graph connectivity

- Computer Science
- Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)
- 1999

This paper shows that space-bounded quantum Turing machines can efficiently simulate a limited class of random processes-random walks on undirected graphs-without relying on measurements during the computation, and demonstrates that the Undirected graph connectivity problem for regular graphs can be solved by one-sided error quantum Turing Machines that run in logspace and require a single measurement at the end of their computations. Expand

On the Power of 2-Way Quantum Finite State AutomataJohn

- 1997

In this paper, we introduce 2-way quantum nite state automata (2qfa's), which are the quantum analogue of deterministic, nondeterministic and probabilistic 2-way nite state automata (2dfa's, 2nfa's… Expand

Logically and Physically Reversible Natural Computing: A Tutorial

- Computer Science
- RC
- 2013

Encouraged by new, experimentally viable DNA computing models, there is a resurgent interest in logically reversible computing by the natural computing community. Expand

#### References

A Taxonomy of Problems with Fast Parallel Algorithms

- Mathematics, Computer Science
- Inf. Control.
- 1985

An attempt is made to identify important subclasses of NC and give interesting examples in each subclass, and a new problem complete for deterministic polynomial time is given, namely, finding the lexicographically first maximal clique in a graph. Expand