[{"type":"conference","citation":{"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.","apa":"Chatterjee, K., &#38; Doyen, L. (2021). Stochastic processes with expected stopping time. In <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i> (pp. 1–13). Rome, Italy: Institute of Electrical and Electronics Engineers. <a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">https://doi.org/10.1109/LICS52264.2021.9470595</a>","ieee":"K. Chatterjee and L. Doyen, “Stochastic processes with expected stopping time,” in <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, Rome, Italy, 2021, pp. 1–13.","ama":"Chatterjee K, Doyen L. Stochastic processes with expected stopping time. In: <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>. Institute of Electrical and Electronics Engineers; 2021:1-13. doi:<a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">10.1109/LICS52264.2021.9470595</a>","chicago":"Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected Stopping Time.” In <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, 1–13. Institute of Electrical and Electronics Engineers, 2021. <a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">https://doi.org/10.1109/LICS52264.2021.9470595</a>.","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.” <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13, doi:<a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">10.1109/LICS52264.2021.9470595</a>."},"quality_controlled":"1","abstract":[{"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.","lang":"eng"}],"publication_status":"published","language":[{"iso":"eng"}],"status":"public","publisher":"Institute of Electrical and Electronics Engineers","day":"07","doi":"10.1109/LICS52264.2021.9470595","arxiv":1,"oa_version":"Preprint","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"full_name":"Doyen, Laurent","last_name":"Doyen","first_name":"Laurent"}],"isi":1,"conference":{"name":"LICS: Symposium on Logic in Computer Science","location":"Rome, Italy","start_date":"2021-06-29","end_date":"2021-07-02"},"year":"2021","publication_identifier":{"eisbn":["978-1-6654-4895-6"],"issn":["1043-6871"],"isbn":["978-1-6654-4896-3"]},"department":[{"_id":"KrCh"}],"scopus_import":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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).","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2104.07278","open_access":"1"}],"project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}],"_id":"10004","date_created":"2021-09-12T22:01:25Z","external_id":{"arxiv":["2104.07278"],"isi":["000947350400036"]},"publication":"Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science","page":"1-13","date_published":"2021-07-07T00:00:00Z","article_processing_charge":"No","keyword":["Computer science","Heuristic algorithms","Memory management","Automata","Markov processes","Probability distribution","Complexity theory"],"ec_funded":1,"date_updated":"2025-07-14T09:10:08Z","title":"Stochastic processes with expected stopping time","month":"07"},{"extern":"1","scopus_import":"1","volume":33,"intvolume":"        33","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1-6","page":"295-308","publication":"Computer Networks","date_created":"2022-07-28T15:11:53Z","_id":"11685","month":"06","date_updated":"2022-09-12T09:09:13Z","title":"On near-uniform URL sampling","article_processing_charge":"No","keyword":["URL sampling","Random walks","Internet domain distribution","Search engine size"],"date_published":"2000-06-01T00:00:00Z","citation":{"chicago":"Henzinger, Monika H, Allan Heydon, Michael Mitzenmacher, and Marc Najork. “On Near-Uniform URL Sampling.” <i>Computer Networks</i>. Elsevier, 2000. <a href=\"https://doi.org/10.1016/s1389-1286(00)00055-4\">https://doi.org/10.1016/s1389-1286(00)00055-4</a>.","ama":"Henzinger MH, Heydon A, Mitzenmacher M, Najork M. On near-uniform URL sampling. <i>Computer Networks</i>. 2000;33(1-6):295-308. doi:<a href=\"https://doi.org/10.1016/s1389-1286(00)00055-4\">10.1016/s1389-1286(00)00055-4</a>","ista":"Henzinger MH, Heydon A, Mitzenmacher M, Najork M. 2000. On near-uniform URL sampling. Computer Networks. 33(1–6), 295–308.","mla":"Henzinger, Monika H., et al. “On Near-Uniform URL Sampling.” <i>Computer Networks</i>, vol. 33, no. 1–6, Elsevier, 2000, pp. 295–308, doi:<a href=\"https://doi.org/10.1016/s1389-1286(00)00055-4\">10.1016/s1389-1286(00)00055-4</a>.","apa":"Henzinger, M. H., Heydon, A., Mitzenmacher, M., &#38; Najork, M. (2000). On near-uniform URL sampling. <i>Computer Networks</i>. Elsevier. <a href=\"https://doi.org/10.1016/s1389-1286(00)00055-4\">https://doi.org/10.1016/s1389-1286(00)00055-4</a>","short":"M.H. Henzinger, A. Heydon, M. Mitzenmacher, M. Najork, Computer Networks 33 (2000) 295–308.","ieee":"M. H. Henzinger, A. Heydon, M. Mitzenmacher, and M. Najork, “On near-uniform URL sampling,” <i>Computer Networks</i>, vol. 33, no. 1–6. Elsevier, pp. 295–308, 2000."},"type":"journal_article","article_type":"original","status":"public","language":[{"iso":"eng"}],"abstract":[{"text":"We consider the problem of sampling URLs uniformly at random from the Web. A tool for sampling URLs uniformly can be used to estimate various properties of Web pages, such as the fraction of pages in various Internet domains or written in various languages. Moreover, uniform URL sampling can be used to determine the sizes of various search engines relative to the entire Web. In this paper, we consider sampling approaches based on random walks of the Web graph. In particular, we suggest ways of improving sampling based on random walks to make the samples closer to uniform. We suggest a natural test bed based on random graphs for testing the effectiveness of our procedures. We then use our sampling approach to estimate the distribution of pages over various Internet domains and to estimate the coverage of various search engine indexes.","lang":"eng"}],"publication_status":"published","quality_controlled":"1","oa_version":"None","doi":"10.1016/s1389-1286(00)00055-4","day":"01","publisher":"Elsevier","publication_identifier":{"issn":["1389-1286"]},"year":"2000","author":[{"first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","last_name":"Henzinger"},{"last_name":"Heydon","full_name":"Heydon, Allan","first_name":"Allan"},{"last_name":"Mitzenmacher","full_name":"Mitzenmacher, Michael","first_name":"Michael"},{"first_name":"Marc","last_name":"Najork","full_name":"Najork, Marc"}]},{"extern":"1","type":"book_chapter","citation":{"ama":"Barton NH. Speciation. In: Myers A, Giller P, eds. <i>Analytical Biogeography: An Integrated Approach to the Study of Animal and Plant Distributions</i>. 1st ed. Springer; 1988:185-218. doi:<a href=\"https://doi.org/10.1007/978-94-009-0435-4\">10.1007/978-94-009-0435-4</a>","chicago":"Barton, Nicholas H. “Speciation.” In <i>Analytical Biogeography: An Integrated Approach to the Study of Animal and Plant Distributions</i>, edited by Alan Myers and Paul Giller, 1st ed., 185–218. Springer, 1988. <a href=\"https://doi.org/10.1007/978-94-009-0435-4\">https://doi.org/10.1007/978-94-009-0435-4</a>.","mla":"Barton, Nicholas H. “Speciation.” <i>Analytical Biogeography: An Integrated Approach to the Study of Animal and Plant Distributions</i>, edited by Alan Myers and Paul Giller, 1st ed., Springer, 1988, pp. 185–218, doi:<a href=\"https://doi.org/10.1007/978-94-009-0435-4\">10.1007/978-94-009-0435-4</a>.","ista":"Barton NH. 1988.Speciation. In: Analytical biogeography: An integrated approach to the study of animal and plant distributions. , 185–218.","apa":"Barton, N. H. (1988). Speciation. In A. Myers &#38; P. Giller (Eds.), <i>Analytical biogeography: An integrated approach to the study of animal and plant distributions</i> (1st ed., pp. 185–218). Springer. <a href=\"https://doi.org/10.1007/978-94-009-0435-4\">https://doi.org/10.1007/978-94-009-0435-4</a>","short":"N.H. Barton, in:, A. Myers, P. Giller (Eds.), Analytical Biogeography: An Integrated Approach to the Study of Animal and Plant Distributions, 1st ed., Springer, 1988, pp. 185–218.","ieee":"N. H. Barton, “Speciation,” in <i>Analytical biogeography: An integrated approach to the study of animal and plant distributions</i>, 1st ed., A. Myers and P. Giller, Eds. Springer, 1988, pp. 185–218."},"scopus_import":"1","quality_controlled":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publist_id":"1736","main_file_link":[{"url":"https://link.springer.com/book/10.1007/978-94-009-0435-4#toc"}],"publication_status":"published","status":"public","language":[{"iso":"eng"}],"publisher":"Springer","_id":"4317","day":"01","date_created":"2018-12-11T12:08:13Z","doi":"10.1007/978-94-009-0435-4","publication":"Analytical biogeography: An integrated approach to the study of animal and plant distributions","oa_version":"None","page":"185 - 218","article_processing_charge":"No","keyword":["biogeography","biology","complexity","distribution","evolution","geology"],"year":"1988","edition":"1","date_published":"1988-01-01T00:00:00Z","author":[{"first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton"}],"editor":[{"full_name":"Myers, Alan","last_name":"Myers","first_name":"Alan"},{"first_name":"Paul","last_name":"Giller","full_name":"Giller, Paul"}],"publication_identifier":{"eissn":["978-94-009-0435-4"],"isbn":["978-0-412-40050-6"]},"title":"Speciation","date_updated":"2022-02-08T09:19:50Z","month":"01"}]