The Halting Probability in Von Neumann Architectures

Abstract. Theoretical models of Turing complete linear genetic programming (GP) programs suggest the fraction of halting programs is vanishingly small. Convergence results proved for an idealised machine, are tested on a small T7 computer with (finite) memory, conditional branches and jumps. Simulations confirm Turing complete fitness landscapes of this type hold at most a vanishingly small fraction of usable solutions.

• Type: Conference
• Year: 2006
• Where: EUROGP
• Authors: William B. Langdon, Riccardo Poli
• Keywords: EUROGP 2006, Linear Genetic Programming, Optimization, Small Fraction, Turing Complete