'algorithm' has 2 meanings: 1. a step-by-step procedure with finite description that halts in finite time 2. an algorithm *for* a function/problem LLMs can fail for both definitions. The first because of human-in-the-loop, the second because they are heuristics at best (no guarantees)
In my work, as in theoretical computer science, we distinguish between (exact) algorithms, heuristics (no guarantees), and approximation algorithm (approx. guarantees) Clear distinctions is relevant in many contexts, for instance this one in cognitive science link.springer.com/article/10.1...