All-Termination(T)

Authors:
Panagiotis Manolios;Aaron Turon
Affiliations:
Northeastern University,;Northeastern University,
Venue:
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Year:
2009

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Abstract

We introduce the All-Termination (T ) problem: given a termination solver T and a collection of functions F , find every subset of the formal parameters to F whose consideration is sufficient to show, using T , that F terminates. An important and motivating application is enhancing theorem proving systems by constructing the set of strongest induction schemes for F , modulo T . These schemes can be derived from the set of termination cores , the minimal sets returned by All-Termination (T ), without any reference to an explicit measure function. We study the All-Termination (T ) problem as applied to the size-change termination analysis ($\mathit{SCT}$), a PSpace -complete problem that underlies many termination solvers. Surprisingly, we show that All-Termination $(\mathit{SCT})$ is also PSpace -complete, even though it substantially generalizes $\mathit{SCT}$. We develop a practical algorithm for All-Termination $(\mathit{SCT})$, and show experimentally that on the ACL2 regression suite (whose size is over 100MB) our algorithm generates stronger induction schemes on 90% of multiargument functions.