Stabilization Without Simplification: A Two-Dimensional Model of Software Evolution

Abstract

Software systems are widely observed to grow in size, complexity, and interdependence over time, yet many large-scale systems remain stable despite persistent structural burden. This apparent tension suggests a limitation in one-dimensional views of software evolution. This paper introduces a graph-based, discrete-time probabilistic framework that separates structural burden from uncertainty. Change effort is modeled as a stochastic variable determined by the dependency neighborhood of the changed entity and by residual variability. Within this framework, burden is defined as expected effort and uncertainty as variance of effort. We show that, under explicit assumptions on non-decreasing average structural load, structural regularization, process stabilization, and covariance control, there exists a regime in which uncertainty decreases while structural burden does not. This regime formalizes the phenomenon of stabilization without simplification. The proposed framework provides a minimal theoretical explanation for how software systems can become more predictable over time without necessarily becoming structurally simpler, and offers a foundation for further theoretical and empirical studies of software evolution.