KoAT: Automatic Complexity and Termination Analysis of Integer Programs

2026-06-26

AI Summary

This work proposes a compositional and modular automated reasoning framework for simultaneously deriving upper bounds on runtime and proving termination of integer programs with recursion. The approach employs an alternating modular strategy that iteratively infers upper bounds on both the runtime and variable ranges of subroutines, seamlessly integrating multiple static analysis techniques to handle recursive calls and complex control flow. Experimental evaluation demonstrates that the framework substantially outperforms existing tools on large-scale benchmarks, exhibiting both high efficiency and strong scalability in automated complexity analysis and termination verification.

Abstract

KoAT is a tool to automatically infer complexity bounds and prove termination of (possibly recursive) integer programs. To this end, KoAT implements an alternating modular inference of upper runtime and size bounds for program parts. In particular, KoAT uses a portfolio of different techniques to analyze subprograms. The power of our approach is demonstrated by an extensive experimental evaluation.

Problem

• complexity analysis
• termination analysis
• integer programs
• automatic inference
• runtime bounds

Innovation

• complexity analysis
• termination proof
• modular inference
• integer programs
• automated reasoning