{"acknowledgement":"We are very thankful to the anonymous reviewers for the helpful and valuable comments. The work was partially supported by the National Natural Science Foundation of China (NSFC) Grant No. 61802254, the Huawei Innovation Research Program, the ERC CoG 863818 (ForM-SMArt), the Facebook PhD Fellowship Program and DOC Fellowship #24956 of the Austrian Academy of Sciences (ÖAW).","status":"public","citation":{"mla":"Wang, Jinyi, et al. “Quantitative Analysis of Assertion Violations in Probabilistic Programs.” <i>Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation</i>, Association for Computing Machinery, 2021, pp. 1171–86, doi:<a href=\"https://doi.org/10.1145/3453483.3454102\">10.1145/3453483.3454102</a>.","ista":"Wang J, Sun Y, Fu H, Chatterjee K, Goharshady AK. 2021. Quantitative analysis of assertion violations in probabilistic programs. Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation. PLDI: Programming Language Design and Implementation, 1171–1186.","short":"J. Wang, Y. Sun, H. Fu, K. Chatterjee, A.K. Goharshady, in:, Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2021, pp. 1171–1186.","ieee":"J. Wang, Y. Sun, H. Fu, K. Chatterjee, and A. K. Goharshady, “Quantitative analysis of assertion violations in probabilistic programs,” in <i>Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation</i>, Online, 2021, pp. 1171–1186.","chicago":"Wang, Jinyi, Yican Sun, Hongfei Fu, Krishnendu Chatterjee, and Amir Kafshdar Goharshady. “Quantitative Analysis of Assertion Violations in Probabilistic Programs.” In <i>Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation</i>, 1171–86. Association for Computing Machinery, 2021. <a href=\"https://doi.org/10.1145/3453483.3454102\">https://doi.org/10.1145/3453483.3454102</a>.","ama":"Wang J, Sun Y, Fu H, Chatterjee K, Goharshady AK. Quantitative analysis of assertion violations in probabilistic programs. In: <i>Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation</i>. Association for Computing Machinery; 2021:1171-1186. doi:<a href=\"https://doi.org/10.1145/3453483.3454102\">10.1145/3453483.3454102</a>","apa":"Wang, J., Sun, Y., Fu, H., Chatterjee, K., &#38; Goharshady, A. K. (2021). Quantitative analysis of assertion violations in probabilistic programs. In <i>Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation</i> (pp. 1171–1186). Online: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3453483.3454102\">https://doi.org/10.1145/3453483.3454102</a>"},"publication":"Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation","month":"06","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2011.14617"}],"publication_status":"published","isi":1,"quality_controlled":"1","doi":"10.1145/3453483.3454102","_id":"9646","year":"2021","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2023-08-10T14:14:08Z","author":[{"first_name":"Jinyi","last_name":"Wang","full_name":"Wang, Jinyi"},{"full_name":"Sun, Yican","first_name":"Yican","last_name":"Sun"},{"id":"3AAD03D6-F248-11E8-B48F-1D18A9856A87","last_name":"Fu","first_name":"Hongfei","full_name":"Fu, Hongfei"},{"first_name":"Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu"},{"full_name":"Goharshady, Amir Kafshdar","last_name":"Goharshady","orcid":"0000-0003-1702-6584","id":"391365CE-F248-11E8-B48F-1D18A9856A87","first_name":"Amir Kafshdar"}],"external_id":{"arxiv":["2011.14617"],"isi":["000723661700076"]},"date_published":"2021-06-01T00:00:00Z","oa_version":"Preprint","conference":{"location":"Online","end_date":"2021-06-26","start_date":"2021-06-20","name":"PLDI: Programming Language Design and Implementation"},"ec_funded":1,"abstract":[{"text":"We consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on the assertion violation probability. The main novelty of our approach is that we prove new and dedicated fixed-point theorems which serve as the theoretical basis of our algorithms and enable us to reason about assertion violation bounds in terms of pre and post fixed-point functions. To synthesize such fixed-points, we devise algorithms that utilize a wide range of mathematical tools, including repulsing ranking supermartingales, Hoeffding's lemma, Minkowski decompositions, Jensen's inequality, and convex optimization. On the theoretical side, we provide (i) the first automated algorithm for lower-bounds on assertion violation probabilities, (ii) the first complete algorithm for upper-bounds of exponential form in affine programs, and (iii) provably and significantly tighter upper-bounds than the previous approaches. On the practical side, we show our algorithms can handle a wide variety of programs from the literature and synthesize bounds that are remarkably tighter than previous results, in some cases by thousands of orders of magnitude.","lang":"eng"}],"oa":1,"department":[{"_id":"KrCh"}],"publisher":"Association for Computing Machinery","type":"conference","project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020"},{"name":"Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies","_id":"267066CE-B435-11E9-9278-68D0E5697425"}],"day":"01","page":"1171-1186","title":"Quantitative analysis of assertion violations in probabilistic programs","article_processing_charge":"No","language":[{"iso":"eng"}],"date_created":"2021-07-11T22:01:18Z","publication_identifier":{"isbn":["9781450383912"]}}