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Deciding Termination of Simple Randomized Loops

Authors Éléanore Meyer , Jürgen Giesl

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Subject Classification

ACM Subject Classification
  • Theory of computation → Probabilistic computation
  • Theory of computation → Program analysis
Keywords
  • decision procedures
  • randomized programs
  • linear loops
  • positive almost sure termination

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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 and Jürgen Giesl. Deciding Termination of Simple Randomized Loops. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 76:1-76:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.76

Author Details

Éléanore Meyer
  • RWTH Aachen University, Germany
Jürgen Giesl
  • RWTH Aachen University, Germany

Funding

DFG Research Training Group 2236 UnRAVeL.

Acknowledgements

We thank Sophia Greiwe for her help with the implementation of our decision procedure in SiRop.

Supplementary Materials

References

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