Method for Proving Loop Termination Using Higher Order Differentials

Abstract

In this paper, we propose a new apporach to proving loop termination that exploits temporal information such as “the value of this expression will always become positive (negative) eventually during iterations”. Considering higher order differentials, it is possible to handle the changes in the values of expressions over multiple consecutive iterations straightforwardly. The proof can be formalized in the ordinal first-order logic framework, and can be automated efficiently using SMT solver through the reduction to satisifiability problem.