Even machines with big databases, which seemingly represent the limit of automata that we could imagine, run into their own limitations.
While each of them can solve for instance the halting problem for a Turing machine, they cannot solve their own version of the halting problem. For example, an Oracle machine cannot answer the question of whether a given Oracle machine will ever halt.
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See that post with different algorithms in metabole
See the journal French Metablog with today different posts
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