Deciding Termination of Simple Randomized Loops
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916819300777984 |
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| author | Meyer, Éléanore Giesl, Jürgen |
| author_facet | Meyer, Éléanore Giesl, Jürgen |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_18541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deciding Termination of Simple Randomized Loops Meyer, Éléanore Giesl, Jürgen Logic in Computer Science 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. |
| title | Deciding Termination of Simple Randomized Loops |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2506.18541 |