TY - JOUR

T1 - Fundamentals of reversible flowchart languages

AU - Yokoyama, Tetsuo

AU - Axelsen, Holger Bock

AU - Glück, Robert

PY - 2016

Y1 - 2016

N2 - Abstract This paper presents the fundamentals of reversible flowcharts. They are intended to naturally represent the structure and control flow of reversible (imperative) programming languages in a simple computation model, in the same way classical flowcharts do for conventional languages. Although reversible flowcharts are superficially similar to classical flowcharts, there are crucial differences: atomic steps are limited to locally invertible operations, and join points require an explicit orthogonalizing conditional expression. Despite these constraints, we show that reversible flowcharts are both expressive and robust: reversible flowcharts can simulate irreversible ones, by adapting reversibilization techniques to the flowchart model. Thus, reversible flowcharts are r-Turing-complete, meaning that they can compute exactly all injective computable functions. Furthermore, structured reversible flowcharts are as expressive as unstructured ones, as shown by a reversible version of the classic Structured Program Theorem. We illustrate how reversible flowcharts can be concretized with two example programming languages, complete with syntax and semantics: a low-level unstructured language and a high-level structured language. We introduce concrete tools such as program inverters and translators for both languages, which follow the structure suggested by the flowchart model. To further illustrate the different concepts and tools brought together in this paper, we present two major worked examples: a reversible permutation-to-code algorithm due to Dijkstra, and a simulation scheme for reversible Turing machines. By exhibiting a wide range of uses we hope that this paper can serve as a springboard for further theoretical research in reversible computing.

AB - Abstract This paper presents the fundamentals of reversible flowcharts. They are intended to naturally represent the structure and control flow of reversible (imperative) programming languages in a simple computation model, in the same way classical flowcharts do for conventional languages. Although reversible flowcharts are superficially similar to classical flowcharts, there are crucial differences: atomic steps are limited to locally invertible operations, and join points require an explicit orthogonalizing conditional expression. Despite these constraints, we show that reversible flowcharts are both expressive and robust: reversible flowcharts can simulate irreversible ones, by adapting reversibilization techniques to the flowchart model. Thus, reversible flowcharts are r-Turing-complete, meaning that they can compute exactly all injective computable functions. Furthermore, structured reversible flowcharts are as expressive as unstructured ones, as shown by a reversible version of the classic Structured Program Theorem. We illustrate how reversible flowcharts can be concretized with two example programming languages, complete with syntax and semantics: a low-level unstructured language and a high-level structured language. We introduce concrete tools such as program inverters and translators for both languages, which follow the structure suggested by the flowchart model. To further illustrate the different concepts and tools brought together in this paper, we present two major worked examples: a reversible permutation-to-code algorithm due to Dijkstra, and a simulation scheme for reversible Turing machines. By exhibiting a wide range of uses we hope that this paper can serve as a springboard for further theoretical research in reversible computing.

KW - r-Turing-completeness

U2 - 10.1016/j.tcs.2015.07.046

DO - 10.1016/j.tcs.2015.07.046

M3 - Journal article

VL - 611

SP - 87

EP - 115

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -