# On the formalization of Asynchronous First Passage Algorithms

## TL;DR

This paper revisits the formalization of First Passage algorithms, identifies a conceptual contradiction, and proposes a new formal framework that clarifies the principles without affecting numerical results.

## Contribution

It introduces a revised formalization of First Passage algorithms that resolves a conceptual contradiction and strengthens the theoretical foundation.

## Key findings

- Numerical results remain unaffected despite the contradiction.
- A new formal framework clarifies the algorithm's principles.
- Numerical evidence supports the revised formalization.

## Abstract

The formalization of First Passage schemes is revisited and the emerging of a conceptual contradiction is underlined. We then show why, despite such a contradiction, the numerical results are not explicitly affected. Through a different formalization of the problem, we recast the current principles of the algorithm in a more solid conceptual framework, and numerical evidence gives further justification to our claims.