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.

Nowadays, the main advances in computational power are due to parallelism. However, most parallel languages have been designed with a focus on processors and threads. This makes dealing with data and memory in programs hard, which distances the implementation from its original algorithm. We propose a new paradigm for parallel programming, the data-autonomous paradigm, where computation is performed by autonomous data elements. Programs in this paradigm are focused on making the data collaborate in a highly parallel fashion. We furthermore present AuDaLa, the first data autonomous programming language, and provide a full formalisation that includes a type system and operational semantics. Programming in AuDaLais very natural, as illustrated by examples, albeit in a style very different from sequential and contemporary parallel programming. Additionally, it lends itself for the formal verification of parallel programs, which we demonstrate.