--- _id: '9646' abstract: - lang: eng 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. 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).' article_processing_charge: No author: - first_name: Jinyi full_name: Wang, Jinyi last_name: Wang - first_name: Yican full_name: Sun, Yican last_name: Sun - first_name: Hongfei full_name: Fu, Hongfei id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87 last_name: Fu - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Amir Kafshdar full_name: Goharshady, Amir Kafshdar id: 391365CE-F248-11E8-B48F-1D18A9856A87 last_name: Goharshady orcid: 0000-0003-1702-6584 citation: ama: 'Wang J, Sun Y, Fu H, Chatterjee K, Goharshady AK. Quantitative analysis of assertion violations in probabilistic programs. In: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation. Association for Computing Machinery; 2021:1171-1186. doi:10.1145/3453483.3454102' apa: 'Wang, J., Sun, Y., Fu, H., Chatterjee, K., & Goharshady, A. K. (2021). Quantitative analysis of assertion violations in probabilistic programs. In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation (pp. 1171–1186). Online: Association for Computing Machinery. https://doi.org/10.1145/3453483.3454102' chicago: Wang, Jinyi, Yican Sun, Hongfei Fu, Krishnendu Chatterjee, and Amir Kafshdar Goharshady. “Quantitative Analysis of Assertion Violations in Probabilistic Programs.” In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, 1171–86. Association for Computing Machinery, 2021. https://doi.org/10.1145/3453483.3454102. ieee: J. Wang, Y. Sun, H. Fu, K. Chatterjee, and A. K. Goharshady, “Quantitative analysis of assertion violations in probabilistic programs,” in Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Online, 2021, pp. 1171–1186. 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.' mla: Wang, Jinyi, et al. “Quantitative Analysis of Assertion Violations in Probabilistic Programs.” Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2021, pp. 1171–86, doi:10.1145/3453483.3454102. 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. conference: end_date: 2021-06-26 location: Online name: 'PLDI: Programming Language Design and Implementation' start_date: 2021-06-20 date_created: 2021-07-11T22:01:18Z date_published: 2021-06-01T00:00:00Z date_updated: 2023-08-10T14:14:08Z day: '01' department: - _id: KrCh doi: 10.1145/3453483.3454102 ec_funded: 1 external_id: arxiv: - '2011.14617' isi: - '000723661700076' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2011.14617 month: '06' oa: 1 oa_version: Preprint page: 1171-1186 project: - _id: 0599E47C-7A3F-11EA-A408-12923DDC885E call_identifier: H2020 grant_number: '863818' name: 'Formal Methods for Stochastic Models: Algorithms and Applications' - _id: 267066CE-B435-11E9-9278-68D0E5697425 name: Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies publication: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation publication_identifier: isbn: - '9781450383912' publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' scopus_import: '1' status: public title: Quantitative analysis of assertion violations in probabilistic programs type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2021' ... --- _id: '9645' abstract: - lang: eng text: "We consider the fundamental problem of reachability analysis over imperative programs with real variables. Previous works that tackle reachability are either unable to handle programs consisting of general loops (e.g. symbolic execution), or lack completeness guarantees (e.g. abstract interpretation), or are not automated (e.g. incorrectness logic). In contrast, we propose a novel approach for reachability analysis that can handle general and complex loops, is complete, and can be entirely automated for a wide family of programs. Through the notion of Inductive Reachability Witnesses (IRWs), our approach extends ideas from both invariant generation and termination to reachability analysis.\r\n\r\nWe first show that our IRW-based approach is sound and complete for reachability analysis of imperative programs. Then, we focus on linear and polynomial programs and develop automated methods for synthesizing linear and polynomial IRWs. In the linear case, we follow the well-known approaches using Farkas' Lemma. Our main contribution is in the polynomial case, where we present a push-button semi-complete algorithm. We achieve this using a novel combination of classical theorems in real algebraic geometry, such as Putinar's Positivstellensatz and Hilbert's Strong Nullstellensatz. Finally, our experimental results show we can prove complex reachability objectives over various benchmarks that were beyond the reach of previous methods." acknowledgement: This research was partially supported by the ERC CoG 863818 (ForM-SMArt), the National Natural Science Foundation of China (NSFC) Grant No. 61802254, the Huawei Innovation Research Program, the Facebook PhD Fellowship Program, and DOC Fellowship No. 24956 of the Austrian Academy of Sciences (ÖAW). article_processing_charge: No author: - first_name: Ali full_name: Asadi, Ali last_name: Asadi - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Hongfei full_name: Fu, Hongfei id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87 last_name: Fu - first_name: Amir Kafshdar full_name: Goharshady, Amir Kafshdar id: 391365CE-F248-11E8-B48F-1D18A9856A87 last_name: Goharshady orcid: 0000-0003-1702-6584 - first_name: Mohammad full_name: Mahdavi, Mohammad last_name: Mahdavi citation: ama: 'Asadi A, Chatterjee K, Fu H, Goharshady AK, Mahdavi M. Polynomial reachability witnesses via Stellensätze. In: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation. Association for Computing Machinery; 2021:772-787. doi:10.1145/3453483.3454076' apa: 'Asadi, A., Chatterjee, K., Fu, H., Goharshady, A. K., & Mahdavi, M. (2021). Polynomial reachability witnesses via Stellensätze. In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation (pp. 772–787). Online: Association for Computing Machinery. https://doi.org/10.1145/3453483.3454076' chicago: Asadi, Ali, Krishnendu Chatterjee, Hongfei Fu, Amir Kafshdar Goharshady, and Mohammad Mahdavi. “Polynomial Reachability Witnesses via Stellensätze.” In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, 772–87. Association for Computing Machinery, 2021. https://doi.org/10.1145/3453483.3454076. ieee: A. Asadi, K. Chatterjee, H. Fu, A. K. Goharshady, and M. Mahdavi, “Polynomial reachability witnesses via Stellensätze,” in Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Online, 2021, pp. 772–787. ista: 'Asadi A, Chatterjee K, Fu H, Goharshady AK, Mahdavi M. 2021. Polynomial reachability witnesses via Stellensätze. Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation. PLDI: Programming Language Design and Implementation, 772–787.' mla: Asadi, Ali, et al. “Polynomial Reachability Witnesses via Stellensätze.” Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2021, pp. 772–87, doi:10.1145/3453483.3454076. short: A. Asadi, K. Chatterjee, H. Fu, A.K. Goharshady, M. Mahdavi, in:, Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2021, pp. 772–787. conference: end_date: 2021-06-26 location: Online name: ' PLDI: Programming Language Design and Implementation' start_date: 2021-06-20 date_created: 2021-07-11T22:01:17Z date_published: 2021-06-01T00:00:00Z date_updated: 2023-08-10T14:13:39Z day: '01' department: - _id: KrCh doi: 10.1145/3453483.3454076 ec_funded: 1 external_id: isi: - '000723661700050' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://hal.archives-ouvertes.fr/hal-03183862/ month: '06' oa: 1 oa_version: Submitted Version page: 772-787 project: - _id: 0599E47C-7A3F-11EA-A408-12923DDC885E call_identifier: H2020 grant_number: '863818' name: 'Formal Methods for Stochastic Models: Algorithms and Applications' - _id: 267066CE-B435-11E9-9278-68D0E5697425 name: Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies publication: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation publication_identifier: isbn: - '9781450383912' publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' scopus_import: '1' status: public title: Polynomial reachability witnesses via Stellensätze type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2021' ... --- _id: '10002' abstract: - lang: eng text: 'We present a faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs). This problem generalizes the SCC decomposition problem of graphs and closed recurrent sets of Markov chains. The model of symbolic algorithms is widely used in formal verification and model-checking, where access to the input model is restricted to only symbolic operations (e.g., basic set operations and computation of one-step neighborhood). For an input MDP with n vertices and m edges, the classical symbolic algorithm from the 1990s for the MEC decomposition requires O(n2) symbolic operations and O(1) symbolic space. The only other symbolic algorithm for the MEC decomposition requires O(nm−−√) symbolic operations and O(m−−√) symbolic space. A main open question is whether the worst-case O(n2) bound for symbolic operations can be beaten. We present a symbolic algorithm that requires O˜(n1.5) symbolic operations and O˜(n−−√) symbolic space. Moreover, the parametrization of our algorithm provides a trade-off between symbolic operations and symbolic space: for all 0<ϵ≤1/2 the symbolic algorithm requires O˜(n2−ϵ) symbolic operations and O˜(nϵ) symbolic space ( O˜ hides poly-logarithmic factors). Using our techniques we present faster algorithms for computing the almost-sure winning regions of ω -regular objectives for MDPs. We consider the canonical parity objectives for ω -regular objectives, and for parity objectives with d -priorities we present an algorithm that computes the almost-sure winning region with O˜(n2−ϵ) symbolic operations and O˜(nϵ) symbolic space, for all 0<ϵ≤1/2 .' acknowledgement: The authors are grateful to the anonymous referees for their valuable comments. A. S. is fully supported by the Vienna Science and Technology Fund (WWTF) through project ICT15–003. K. C. is supported by the Austrian Science Fund (FWF) NFN Grant No S11407-N23 (RiSE/SHiNE) and by the ERC CoG 863818 (ForM-SMArt). For M. H. the research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP/2007–2013) / ERC Grant Agreement no. 340506. article_processing_charge: No author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Wolfgang full_name: Dvorak, Wolfgang last_name: Dvorak - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Alexander full_name: Svozil, Alexander last_name: Svozil citation: ama: 'Chatterjee K, Dvorak W, Henzinger MH, Svozil A. Symbolic time and space tradeoffs for probabilistic verification. In: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science. Institute of Electrical and Electronics Engineers; 2021:1-13. doi:10.1109/LICS52264.2021.9470739' apa: 'Chatterjee, K., Dvorak, W., Henzinger, M. H., & Svozil, A. (2021). Symbolic time and space tradeoffs for probabilistic verification. In Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science (pp. 1–13). Rome, Italy: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/LICS52264.2021.9470739' chicago: Chatterjee, Krishnendu, Wolfgang Dvorak, Monika H Henzinger, and Alexander Svozil. “Symbolic Time and Space Tradeoffs for Probabilistic Verification.” In Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, 1–13. Institute of Electrical and Electronics Engineers, 2021. https://doi.org/10.1109/LICS52264.2021.9470739. ieee: K. Chatterjee, W. Dvorak, M. H. Henzinger, and A. Svozil, “Symbolic time and space tradeoffs for probabilistic verification,” in Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Rome, Italy, 2021, pp. 1–13. ista: 'Chatterjee K, Dvorak W, Henzinger MH, Svozil A. 2021. Symbolic time and space tradeoffs for probabilistic verification. Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Symposium on Logic in Computer Science, 1–13.' mla: Chatterjee, Krishnendu, et al. “Symbolic Time and Space Tradeoffs for Probabilistic Verification.” Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13, doi:10.1109/LICS52264.2021.9470739. short: K. Chatterjee, W. Dvorak, M.H. Henzinger, A. Svozil, in:, Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13. conference: end_date: 2021-07-02 location: Rome, Italy name: 'LICS: Symposium on Logic in Computer Science' start_date: 2021-06-29 date_created: 2021-09-12T22:01:24Z date_published: 2021-07-07T00:00:00Z date_updated: 2023-08-14T06:51:33Z day: '07' department: - _id: KrCh doi: 10.1109/LICS52264.2021.9470739 ec_funded: 1 external_id: arxiv: - '2104.07466' isi: - '000947350400089' isi: 1 keyword: - Computer science - Computational modeling - Markov processes - Probabilistic logic - Formal verification - Game Theory language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2104.07466 month: '07' oa: 1 oa_version: Preprint page: 1-13 project: - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory - _id: 0599E47C-7A3F-11EA-A408-12923DDC885E call_identifier: H2020 grant_number: '863818' name: 'Formal Methods for Stochastic Models: Algorithms and Applications' publication: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science publication_identifier: eisbn: - 978-1-6654-4895-6 isbn: - 978-1-6654-4896-3 issn: - 1043-6871 publication_status: published publisher: Institute of Electrical and Electronics Engineers quality_controlled: '1' scopus_import: '1' status: public title: Symbolic time and space tradeoffs for probabilistic verification type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2021' ... --- _id: '10004' abstract: - lang: eng text: 'Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.' acknowledgement: We are grateful to the anonymous reviewers of LICS 2021 and of a previous version of this paper for insightful comments that helped improving the presentation. This research was partially supported by the grant ERC CoG 863818 (ForM-SMArt). article_processing_charge: No author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Laurent full_name: Doyen, Laurent last_name: Doyen citation: ama: 'Chatterjee K, Doyen L. Stochastic processes with expected stopping time. In: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science. Institute of Electrical and Electronics Engineers; 2021:1-13. doi:10.1109/LICS52264.2021.9470595' apa: 'Chatterjee, K., & Doyen, L. (2021). Stochastic processes with expected stopping time. In Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science (pp. 1–13). Rome, Italy: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/LICS52264.2021.9470595' chicago: Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected Stopping Time.” In Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, 1–13. Institute of Electrical and Electronics Engineers, 2021. https://doi.org/10.1109/LICS52264.2021.9470595. ieee: K. Chatterjee and L. Doyen, “Stochastic processes with expected stopping time,” in Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Rome, Italy, 2021, pp. 1–13. ista: 'Chatterjee K, Doyen L. 2021. Stochastic processes with expected stopping time. Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Symposium on Logic in Computer Science, 1–13.' mla: Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected Stopping Time.” Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13, doi:10.1109/LICS52264.2021.9470595. short: K. Chatterjee, L. Doyen, in:, Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13. conference: end_date: 2021-07-02 location: Rome, Italy name: 'LICS: Symposium on Logic in Computer Science' start_date: 2021-06-29 date_created: 2021-09-12T22:01:25Z date_published: 2021-07-07T00:00:00Z date_updated: 2023-08-14T06:52:07Z day: '07' department: - _id: KrCh doi: 10.1109/LICS52264.2021.9470595 ec_funded: 1 external_id: arxiv: - '2104.07278' isi: - '000947350400036' isi: 1 keyword: - Computer science - Heuristic algorithms - Memory management - Automata - Markov processes - Probability distribution - Complexity theory language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2104.07278 month: '07' oa: 1 oa_version: Preprint page: 1-13 project: - _id: 0599E47C-7A3F-11EA-A408-12923DDC885E call_identifier: H2020 grant_number: '863818' name: 'Formal Methods for Stochastic Models: Algorithms and Applications' publication: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science publication_identifier: eisbn: - 978-1-6654-4895-6 isbn: - 978-1-6654-4896-3 issn: - 1043-6871 publication_status: published publisher: Institute of Electrical and Electronics Engineers quality_controlled: '1' scopus_import: '1' status: public title: Stochastic processes with expected stopping time type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2021' ... --- _id: '10055' abstract: - lang: eng text: "Repeated idempotent elements are commonly used to characterise iterable behaviours in abstract models of computation. Therefore, given a monoid M, it is natural to ask how long a sequence of elements of M needs to be to ensure the presence of consecutive idempotent factors. This question is formalised through the notion of the Ramsey function R_M associated to M, obtained by mapping every k ∈ ℕ to the minimal integer R_M(k) such that every word u ∈ M^* of length R_M(k) contains k consecutive non-empty factors that correspond to the same idempotent element of M. In this work, we study the behaviour of the Ramsey function R_M by investigating the regular \U0001D49F-length of M, defined as the largest size L(M) of a submonoid of M isomorphic to the set of natural numbers {1,2, …, L(M)} equipped with the max operation. We show that the regular \U0001D49F-length of M determines the degree of R_M, by proving that k^L(M) ≤ R_M(k) ≤ (k|M|⁴)^L(M). To allow applications of this result, we provide the value of the regular \U0001D49F-length of diverse monoids. In particular, we prove that the full monoid of n × n Boolean matrices, which is used to express transition monoids of non-deterministic automata, has a regular \U0001D49F-length of (n²+n+2)/2." acknowledgement: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. I wish to thank Michaël Cadilhac, Emmanuel Filiot and Charles Paperman for their valuable insights concerning Green’s relations. alternative_title: - LIPIcs article_number: '44' article_processing_charge: No author: - first_name: Ismael R full_name: Jecker, Ismael R id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425 last_name: Jecker citation: ama: 'Jecker IR. A Ramsey theorem for finite monoids. In: 38th International Symposium on Theoretical Aspects of Computer Science. Vol 187. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.STACS.2021.44' apa: 'Jecker, I. R. (2021). A Ramsey theorem for finite monoids. In 38th International Symposium on Theoretical Aspects of Computer Science (Vol. 187). Saarbrücken, Germany: Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.STACS.2021.44' chicago: Jecker, Ismael R. “A Ramsey Theorem for Finite Monoids.” In 38th International Symposium on Theoretical Aspects of Computer Science, Vol. 187. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.STACS.2021.44. ieee: I. R. Jecker, “A Ramsey theorem for finite monoids,” in 38th International Symposium on Theoretical Aspects of Computer Science, Saarbrücken, Germany, 2021, vol. 187. ista: 'Jecker IR. 2021. A Ramsey theorem for finite monoids. 38th International Symposium on Theoretical Aspects of Computer Science. STACS: Symposium on Theoretical Aspects of Computer Science, LIPIcs, vol. 187, 44.' mla: Jecker, Ismael R. “A Ramsey Theorem for Finite Monoids.” 38th International Symposium on Theoretical Aspects of Computer Science, vol. 187, 44, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.STACS.2021.44. short: I.R. Jecker, in:, 38th International Symposium on Theoretical Aspects of Computer Science, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. conference: end_date: 2021-03-19 location: Saarbrücken, Germany name: 'STACS: Symposium on Theoretical Aspects of Computer Science' start_date: 2021-03-16 date_created: 2021-09-27T14:33:15Z date_published: 2021-03-10T00:00:00Z date_updated: 2023-08-14T07:03:23Z day: '10' ddc: - '000' department: - _id: KrCh doi: 10.4230/LIPIcs.STACS.2021.44 ec_funded: 1 external_id: isi: - '000635691700044' file: - access_level: open_access checksum: 17432a05733f408de300e17e390a90e4 content_type: application/pdf creator: cchlebak date_created: 2021-10-01T09:55:00Z date_updated: 2021-10-01T09:55:00Z file_id: '10063' file_name: 2021_LIPIcs_Jecker.pdf file_size: 720250 relation: main_file success: 1 file_date_updated: 2021-10-01T09:55:00Z has_accepted_license: '1' intvolume: ' 187' isi: 1 language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '03' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 38th International Symposium on Theoretical Aspects of Computer Science publication_identifier: isbn: - 978-3-9597-7180-1 issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: A Ramsey theorem for finite monoids tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 187 year: '2021' ...