A Gödel machine is a hypothetical self-improving computer program that solves problems in an optimal way.
[1][2] The machine was invented by Jürgen Schmidhuber (first proposed in 2003[3]), but is named after Kurt Gödel who inspired the mathematical theories.
[6] The Gödel machine is often compared with Marcus Hutter's AIXI, another formal specification for an artificial general intelligence.
Schmidhuber points out that the Gödel machine could start out by implementing AIXItl as its initial sub-program, and self-modify after it finds proof that another algorithm for its search code will be better.
[7] Traditional problems solved by a computer only require one input and provide some output.
[7] This does not take into account the dynamic natural environment, and thus was a goal for the Gödel machine to overcome.
Hence even a Gödel machine with unlimited computational resources must ignore those self-improvements whose effectiveness it cannot prove.
denotes the conditional expectation operator with respect to some possibly unknown distribution
[3] Note that we take into account the possibility of extending the expected lifespan through appropriate actions.
Below is the initial axiom scheme: Takes in the index k of an inference rule (such as Modus tollens, Modus ponens), and attempts to apply it to the two previously proved theorems m and n. The resulting theorem is then added to the proof.
This helps to mitigate storage constraints caused by redundant and unnecessary theorems.
Replaces switchprog S pm:n, provided it is a non-empty substring of S p. Verifies whether the goal of the proof search has been reached.
The initial input to the Gödel machine is the representation of a connected graph with a large number of nodes linked by edges of various lengths.
The by-product of maximizing expected reward is to find the shortest path findable within the limited time, given the initial bias.
[3] Prove or disprove as quickly as possible that all even integers > 2 are the sum of two primes (Goldbach’s conjecture).
It is rewarded in proportion to its lifetime, and dies after at most 100 years or as soon as its tank is empty or it falls off a cliff, and so on.