WHOSE HISTORY IS INDEPENDENT OF THE ORDER OF ASYNCHRONOUS UPDATING?

Title: WHOSE HISTORY IS INDEPENDENT OF THE ORDER OF ASYNCHRONOUS UPDATING?

Research Question: Can we determine when the history of a system, where multiple processes are updated in an arbitrary order, is independent of the order in which the updates occur?

Methodology: The researchers propose a method to analyze the system by introducing the concept of invariant histories. They define a sequence of states that is independent of the order of updates and introduce the concept of commutativity, which is a simple sufficient condition for invariant histories.

Results: The researchers prove that the invariant history property is typically undecidable, but they provide a useful simple sufficient condition called commutativity. They demonstrate that this fact is derivable from known results on the confluence of term-rewriting systems, providing a self-contained proof.

Implications: The results of this research have significant implications for the field of computer science and theoretical physics. It provides a new approach to analyzing systems with concurrent processes, which can lead to more efficient and accurate models. Additionally, the concepts and techniques developed in this research can be applied to other areas, such as artificial intelligence and complex systems.

In conclusion, the research question has been addressed by proposing a method to analyze the system and proving a simple sufficient condition for invariant histories. The results have significant implications for the field of computer science and theoretical physics, and the research can be applied to other areas as well.

Link to Article: https://arxiv.org/abs/0101026v1 Authors: arXiv ID: 0101026v1