Stability: An Abstract Domain for the Trend of Variation of Numerical Variables

State-of-the-art abstract domains for static analysis typically focus on over-approximating either the values a variable can hold at a specific program point or the relational dependencies among variables. In this paper, we aim to capture the trend of numerical values during program executions (e.g., increasing, decreasing, or stable) relative to preceding states. By integrating the Stability domain with numerical domains, we can verify co-/contra-variance relationships among potentially unrelated variables. This approach has promising applications for anomaly detection in complex software systems, and for the verification of functional requirements.