Minimal Programs Are Almost Optimal
نویسندگان
چکیده
According to the Algorithmic Coding Theorem, minimal programs of any universal machine are prefix-codes asymptotically optimal with respect to the machine algorithmic probabilities. A stronger version of this result will be proven for a class of machines, not necessarily universal, and any semi-distribution. Furthermore, minimal programs with respect to universal machines will be shown to be almost optimal for any semicomputable semi-distribution. Finally, a complete characterization of all machines satisfying the Algorithmic Coding Theorem is given. Indexed Terms–Minimal program, prefixcode, Chaitin machine, program-size complexity, entropy, Noiseless Coding Theorem, Algorithmic Coding Theorem.
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