Behavioural Theory of Reflective Algorithms II: Reflective Parallel Algorithms

TL;DR

This paper introduces a formal behavioural theory for reflective parallel algorithms that can modify their own behavior, using an abstract machine model called reflective ASM, which captures the class of such algorithms.

Contribution

It develops a comprehensive set of postulates and an abstract machine model for reflective parallel algorithms, extending existing ASM frameworks with self-representation capabilities.

Findings

All reflective parallel algorithms are captured by the rASM model.

The theory preserves bounded exploration using multiset comprehension.

The model enables formal reasoning about self-modifying parallel algorithms.

Abstract

We develop a behavioural theory of reflective parallel algorithms (RAs), i.e. synchronous parallel algorithms that can modify their own behaviour. The theory comprises a set of postulates defining the class of RAs, an abstract machine model, and the proof that all RAs are captured by this machine model. RAs are sequential-time, parallel algorithms, where every state includes a representation of the algorithm in that state, thus enabling linguistic reflection. Bounded exploration is preserved using multiset comprehension terms as values. The abstract machine model is defined by reflective Abstract State Machines (rASMs), which extend ASMs using extended states that include an updatable representation of the main ASM rule to be executed by the machine in that state.