Reversible Two-Party Computations

Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the computation back and forth. We study the computational capacity of such devices and obtain on the one hand that there are regular languages that cannot be accepted by such systems. On the other hand, such systems can accept even non-semilinear languages. Since the systems communicate by sending messages, we consider also systems where the number of messages sent during a computation is restricted. We obtain a finite hierarchy with respect to the allowed amount of communication inside the reversible classes and separations to general, not necessarily reversible, classes. Finally, we study closure properties and decidability questions and obtain that the questions of emptiness, finiteness, inclusion, and equivalence are not semidecidable if a superlogarithmic amount of communication is allowed.Comment: In Proceedings AFL 2023, arXiv:2309.0112

Concise representations of reversible automata

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 exponentially smaller than the size of the explicit representations of corresponding reversible automata. Using those representations it is possible to simulate the computations of reversible automata without explicitly writing down their complete descriptions