Efficient Markov Chain Model of Machine Code Program Execution and Halting

Abstract

We focus on the halting probability and the number ofinstructions executed by programs that halt forTuring-complete register based machines. The formerrepresents the fraction of programs which provideuseful results in a machine code genetic programmingsystem. The latter determines run time and whether ornot the distribution of program functionality hasreached a fixed-point. We describe a Markov chain modelof program execution and halting which accurately fitsempirical data allowing us to efficiently estimate thehalting probability and the numbers of instructionsexecuted for programs including millions ofinstructions. We also discuss how this model can beapplied to improve GP practice.