DynamiTe: Dynamic Termination and Non-termination Proofs

TL;DR

DynamiTe introduces a unified dynamic analysis approach for proving termination and non-termination of non-linear programs by inferring ranking functions and recurrent sets, leveraging mutual information between static and dynamic strategies.

Contribution

The paper presents an integrated algorithm that combines static and dynamic analysis to improve termination and non-termination proofs for non-linear programs.

Findings

Successfully infers ranking functions from concrete transitive closures.

Dynamically learns conditions to refine recurrent sets.

Mutually informs static and dynamic strategies for better analysis.

Abstract

There is growing interest in termination reasoning for non-linear programs and, meanwhile, recent dynamic strategies have shown they are able to infer invariants for such challenging programs. These advances led us to hypothesize that perhaps such dynamic strategies for non-linear invariants could be adapted to learn recurrent sets (for non-termination) and/or ranking functions (for termination). In this paper, we exploit dynamic analysis and draw termination and non-termination as well as static and dynamic strategies closer together in order to tackle non-linear programs. For termination, our algorithm infers ranking functions from concrete transitive closures, and, for non-termination, the algorithm iteratively collects executions and dynamically learns conditions to refine recurrent sets. Finally, we describe an integrated algorithm that allows these algorithms to mutually inform each other, taking counterexamples from a failed validation in one endeavor and crossing both the static/dynamic and termination/non-termination lines, to create new execution samples for the other one.