Scaling of program fitness spaces

Area of Science:

• Computer Science
• Computational Theory
• Program Synthesis

Background:

• Understanding program fitness distribution is crucial for program synthesis and optimization.
• Previous research has explored program fitness landscapes, but scaling with program size remains an open question.

Purpose of the Study:

• To investigate the distribution of program fitness, focusing on parse tree representations.
• To determine how fitness distributions scale with respect to program size.

Main Methods:

• Utilized a combination of program enumeration and Monte Carlo sampling.
• Analyzed a large number of problems across three diverse domains.
• Theoretically proved findings for linear programs and side-effect-free parse trees.

Main Results:

• Program fitness distribution is largely independent of program length beyond a minimum size threshold.
• Demonstrated this independence for linear programs and simple side-effect-free parse trees.
• Quantified the density of solutions for parity problems in XOR-based program trees.

Conclusions:

• Program size has a limited impact on fitness distribution once a program reaches a sufficient complexity.
• The observed independence suggests general principles in program fitness landscapes.
• Preliminary results indicate this may extend to programs with side effects and iteration.