Expressivity of AuDaLa: Turing Completeness and Possible Extensions

TL;DR

This paper demonstrates that AuDaLa, a new data autonomous programming language, is Turing complete and explores extensions to enhance its practical expressivity and performance.

Contribution

It proves AuDaLa's Turing completeness and proposes extensions to improve its practical applicability and efficiency.

Findings

AuDaLa can implement Turing machines correctly.

Extensions can increase AuDaLa's practical expressivity.

Extensions enable better matching of conventional parallel languages.

Abstract

AuDaLa is a recently introduced programming language that follows the new data autonomous paradigm. In this paradigm, small pieces of data execute functions autonomously. Considering the paradigm and the design choices of AuDaLa, it is interesting to determine the expressivity of the language. In this paper, we implement Turing machines in AuDaLa and prove that implementation correct. This proves that AuDaLa is Turing complete, giving an initial indication of AuDaLa's expressivity. Additionally, we give examples of how to add extensions to AuDaLa to increase its practical expressivity and to better match conventional parallel languages, allowing for a more straightforward and performant implementation of algorithms.