Reversible Two-Party Computations

TL;DR

This paper investigates the computational power and limitations of reversible two-party automata systems, revealing their ability to accept complex languages and the impact of communication restrictions on decidability.

Contribution

It introduces a formal model of reversible two-party automata, analyzes their language acceptance capabilities, and explores the effects of communication limits on computational properties.

Findings

Reversible automata can accept non-semilinear languages.

There exists a hierarchy based on communication limits.

Decidability of certain properties fails with superlogarithmic communication.

Abstract

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.