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arXiv · 2506.18541

Deciding Termination of Simple Randomized Loops

Éléanore Meyer·Jürgen Giesl
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Abstract

We show that universal positive almost sure termination (UPAST) is decidable for a class of simple randomized programs, i.e., it is decidable whether the expected runtime of such a program is finite for all inputs. Our class contains all programs that consist of a single loop, with a linear loop guard and a loop body composed of two linear commuting and diagonalizable updates. In each iteration of the loop, the update to be carried out is picked at random, according to a fixed probability. We show the decidability of UPAST for this class of programs, where the program's variables and inputs may range over various sub-semirings of the real numbers. In this way, we extend a line of research initiated by Tiwari in 2004 into the realm of randomized programs.

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Éléanore Meyer, Jürgen Giesl. 2025-06-23. Deciding Termination of Simple Randomized Loops. https://arxiv.org/abs/2506.18541

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