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Alternative Relaxed Target Theorem

We may replace the target theorem (2) (Item 5) by the following alternative target theorem:
(u[s({\bf t_1}) \oplus (switchbit({\bf t_1})=\lq 1\textrm{'}), ...
... \oplus (switchbit({\bf t_1})=\lq 0\textrm{'}), Env({\bf t_1})] )
\end{displaymath} (3)

The only difference to the original target theorem (2) is that the ``$>$'' sign became a ``$\geq$'' sign. That is, the Gödel machine will change itself as soon as it has found a proof that the change will not make things worse. A Global Optimality Theorem similar to Theorem 4.1 holds; simply replace the last phrase in Theorem 4.1 by: the utility of starting the execution of the present switchprog is at least as high as the utility of waiting for the proof searcher to produce an alternative switchprog later.

Juergen Schmidhuber 2005-01-03