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Perplexed comments on John Baez Interviews with Eliezer (Parts 2 and 3) - Less Wrong
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A deterministic algorithm, if run twice with the same inputs, follows the same steps and produces the same outputs each time. A non-deterministic algorithm will not necessarily follow the same steps, and may not even generate the same result.
It has been part of the folklore since Dijkstra's "A Discipline of Programming" that well-written non-deterministic programs may be even easier to understand and prove correct than their deterministic counterparts.