The proofs that every "recursive function" we can calculate by hand we can compute by machine and vice versa—note the usage of the words calculate versus compute -- is remarkable.
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- The proofs that every "recursive function" we can calculate by hand we can compute by machine and vice versa—note the usage of the words calculate versus compute -- is remarkable. But this equivalence together with the thesis (hypothesis, unproven assertion) that this includes every calculation/computation indicates why so much emphasis has been placed upon the use of Turing-equivalent machines in the definition of specific algorithms, and why the definition of "algorithm" itself often refers back to "the Turing machine". This is discussed in more detail under Stephen Kleene's characterization. The following are summaries of the more famous characterizations (Kleene, Markov, Knuth) together with those that introduce novel elements—elements that further expand the definition or contribute to a more precise definition.
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- The proofs that every "recursive function" we can calculate by hand we can compute by machine and vice versa—note the usage of the words calculate versus compute -- is remarkable.
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- Algorithm characterizations
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