Complex Systems

Dissipative Arithmetic Download PDF

William B. Langdon
Department of Computer Science
University College London
Gower Street, London WC1E 6BT, UK


Large arithmetic expressions are dissipative: they lose information and are robust to perturbations. Lack of conservation gives resilience to fluctuations. The limited precision of floating point and the mixture of linear and nonlinear operations make such functions anti-fragile and give a largely stable locally flat plateau a rich fitness landscape. This slows long-term evolution of complex programs, suggesting a need for depth-aware crossover and mutation operators in tree-based genetic programming. It also suggests that deeply nested computer program source code is error tolerant because disruptions tend to fail to propagate, and therefore the optimal placement of test oracles is as close to software defects as practical.

Keywords: information loss; irreversible computing; entropy; evolvability; arithmetic; software mutational robustness; optimal test oracle placement; evolution of complexity; data dependent computational irreducibility; effective computational equivalence; experimental mathematics; algorithmic information dynamics

Cite this publication as:
W. B. Langdon, “Dissipative Arithmetic,” Complex Systems, 31(3), 2022 pp. 287–309.