The halting probability in von neumann architectures

Authors:
W. B. Langdon;R. Poli
Affiliations:
Department of Computer Science, University of Essex, UK;Department of Computer Science, University of Essex, UK
Venue:
EuroGP'06 Proceedings of the 9th European conference on Genetic Programming
Year:
2006

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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.