conference paper published yes Krishnendu Chatterjee author 2E5DCA20-F248-11E8-B48F-1D18A9856A870000-0002-4561-241X Amir Kafshdar Goharshady author 391365CE-F248-11E8-B48F-1D18A9856A870000-0003-1702-6584 Tobias Meggendorfer author b21b0c15-30a2-11eb-80dc-f13ca25802e10000-0002-1712-2165 Dorde Zikelic author 294AA7A6-F248-11E8-B48F-1D18A9856A870000-0002-4681-1699 KrCh department CAV: Computer Aided Verification Formal Methods for Stochastic Models: Algorithms and Applications project International IST Doctoral Program project We consider the quantitative problem of obtaining lower-bounds on the probability of termination of a given non-deterministic probabilistic program. Specifically, given a non-termination threshold p∈[0,1], we aim for certificates proving that the program terminates with probability at least 1−p. The basic idea of our approach is to find a terminating stochastic invariant, i.e. a subset SI of program states such that (i) the probability of the program ever leaving SI is no more than p, and (ii) almost-surely, the program either leaves SI or terminates. While stochastic invariants are already well-known, we provide the first proof that the idea above is not only sound, but also complete for quantitative termination analysis. We then introduce a novel sound and complete characterization of stochastic invariants that enables template-based approaches for easy synthesis of quantitative termination certificates, especially in affine or polynomial forms. Finally, by combining this idea with the existing martingale-based methods that are relatively complete for qualitative termination analysis, we obtain the first automated, sound, and relatively complete algorithm for quantitative termination analysis. Notably, our completeness guarantees for quantitative termination analysis are as strong as the best-known methods for the qualitative variant. Our prototype implementation demonstrates the effectiveness of our approach on various probabilistic programs. We also demonstrate that our algorithm certifies lower bounds on termination probability for probabilistic programs that are beyond the reach of previous methods. https://research-explorer.ista.ac.at/download/12000/12003/2022_LNCS_Chatterjee.pdf application/pdfno Springer2022Haifa, Israel eng 0302-9743 1611-3349 9783031131844 00087030450000410.1007/978-3-031-13185-1_4 1337155-78 https://research-explorer.ista.ac.at/record/14539 Chatterjee, K., Goharshady, A. K., Meggendorfer, T., &#38; Zikelic, D. (2022). Sound and complete certificates for auantitative termination analysis of probabilistic programs. In <i>Proceedings of the 34th International Conference on Computer Aided Verification</i> (Vol. 13371, pp. 55–78). Haifa, Israel: Springer. <a href="https://doi.org/10.1007/978-3-031-13185-1_4">https://doi.org/10.1007/978-3-031-13185-1_4</a> Chatterjee, Krishnendu, Amir Kafshdar Goharshady, Tobias Meggendorfer, and Dorde Zikelic. “Sound and Complete Certificates for Auantitative Termination Analysis of Probabilistic Programs.” In <i>Proceedings of the 34th International Conference on Computer Aided Verification</i>, 13371:55–78. Springer, 2022. <a href="https://doi.org/10.1007/978-3-031-13185-1_4">https://doi.org/10.1007/978-3-031-13185-1_4</a>. Chatterjee K, Goharshady AK, Meggendorfer T, Zikelic D. 2022. Sound and complete certificates for auantitative termination analysis of probabilistic programs. Proceedings of the 34th International Conference on Computer Aided Verification. CAV: Computer Aided Verification, LNCS, vol. 13371, 55–78. Chatterjee K, Goharshady AK, Meggendorfer T, Zikelic D. Sound and complete certificates for auantitative termination analysis of probabilistic programs. In: <i>Proceedings of the 34th International Conference on Computer Aided Verification</i>. Vol 13371. Springer; 2022:55-78. doi:<a href="https://doi.org/10.1007/978-3-031-13185-1_4">10.1007/978-3-031-13185-1_4</a> K. Chatterjee, A. K. Goharshady, T. Meggendorfer, and D. Zikelic, “Sound and complete certificates for auantitative termination analysis of probabilistic programs,” in <i>Proceedings of the 34th International Conference on Computer Aided Verification</i>, Haifa, Israel, 2022, vol. 13371, pp. 55–78. Chatterjee, Krishnendu, et al. “Sound and Complete Certificates for Auantitative Termination Analysis of Probabilistic Programs.” <i>Proceedings of the 34th International Conference on Computer Aided Verification</i>, vol. 13371, Springer, 2022, pp. 55–78, doi:<a href="https://doi.org/10.1007/978-3-031-13185-1_4">10.1007/978-3-031-13185-1_4</a>. K. Chatterjee, A.K. Goharshady, T. Meggendorfer, D. Zikelic, in:, Proceedings of the 34th International Conference on Computer Aided Verification, Springer, 2022, pp. 55–78. 120002022-08-28T22:02:02Z2026-04-07T13:27:55Z