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**
Jürgen Schmidhuber
juergen@idsia.ch - http://www.idsia.ch/~juergen
IDSIA, Galleria 2, 6928 Manno (Lugano), Switzerland **

**25 September 2003**

A Gödel machine solves general
computational problems in a possibly
stochastic and reactive environment.
Its initial software includes an axiomatic description of
(1) the Gödel machine's hardware,
(2) known aspects of the environment,
(3) goals and rewards to be achieved,
(4) costs of actions and computations,
(5) the initial software itself (no circularity involved here).
It also includes a possibly sub-optimal
initial problem-solving policy and a proof searcher
searching the space of computable proof
techniques--that is, programs whose outputs are proofs.
Unlike previous approaches,
the self-referential Gödel machine will rewrite *any* part of its
software (including axioms and proof searcher)
as soon as it has found a proof that this will improve its
future performance. By definition,
it produces optimal self-improvements,
given arbitrary formalized problems
and typically limited computational resources;
its optimality notion is not
restricted to the concept of *asymptotic* optimality.
To initialize the proof searcher we may use the recent
Optimal Ordered Problem Solver.

- Introduction: Basic Principles of Gödel Machines
- Formal Details of a Particular Gödel Machine
- Overview of Hardware and Initial Software / Proof Searcher
- How Online Proof Techniques Connect Syntax and Semantics
- Bias-Optimal Proof Search (BIOPS)

- Discussion
- Possible Types of Gödel Machine Self-Improvements
- Example Applications
- Probabilistic Gödel Machine Hardware
- Limitations of the Gödel machine
- More Relations to Previous Work on Self-Improving Machines
- Practical Issues
- Are Humans Probabilistic Gödel Machines?

- Summary / Conclusion
- Acknowledgments
- Bibliography
- About this document ...

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