All-Termination(T)
نویسندگان
چکیده
We introduce the All-Termination(T ) problem: given a termination solver, T , and a program (a set of functions), find every set of formal arguments whose consideration is sufficient to show the program terminating using T . One important and motivating application is enhancing theorem proving systems by constructing the set of strongest induction schemes for a program, modulo T . These schemes can be derived from the set of termination cores, the minimal sets returned by All-Termination(T ). We study the All-Termination(T ) problem as applied to two existing termination analyses: general size-change (SCT ) and polynomial size-change (SCP). We analyze the intrinsic complexity of the problems and develop algorithms that we expect to perform well in practice. We show that All-Termination(SCT ) is a PSpacecomplete problem. We also show that no output-polynomial algorithm exists for AllTermination(SCP) (unless P = NP). Finally, we develop practical algorithms, some based on SAT-solving, for both problems.
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