Reversible pushdown automata

Reversible pushdown automata are deterministic pushdown automata that are also backward deterministic. Therefore, they have the property that any configuration occurring in any computation has exactly one predecessor. In this paper, the computational capacity of reversible computations in pushdown automata is investigated and turns out to lie properly in between the regular and deterministic context-free languages. Furthermore, it is shown that a deterministic context-free language cannot be accepted reversibly if more than realtime is necessary for acceptance. Closure properties as well as decidability questions for reversible pushdown automata are studied. Finally, we show that the problem to decide whether a given nondeterministic or deterministic pushdown automaton is reversible is P-complete, whereas it is undecidable whether the language accepted by a given nondeterministic pushdown automaton is reversible.

► The computational capacity of reversible PDA lies properly in between DFA and DPDA. ► There are non-realtime deterministic context-free languages which are not accepted. ► Closure properties and decidability questions are studied. ► To decide reversibility of a nondeterministic or deterministic PDA is P-complete. ► It is undecidable whether a context-free language is reversible.