[{"language":[{"iso":"eng"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"5","citation":{"chicago":"Avni, Guy, Ismael R Jecker, and Dorde Zikelic. “Bidding Graph Games with Partially-Observable Budgets.” In <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>, 37:5464–71, 2023. <a href=\"https://doi.org/10.1609/aaai.v37i5.25679\">https://doi.org/10.1609/aaai.v37i5.25679</a>.","ista":"Avni G, Jecker IR, Zikelic D. 2023. Bidding graph games with partially-observable budgets. Proceedings of the 37th AAAI Conference on Artificial Intelligence. AAAI: Conference on Artificial Intelligence vol. 37, 5464–5471.","apa":"Avni, G., Jecker, I. R., &#38; Zikelic, D. (2023). Bidding graph games with partially-observable budgets. In <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i> (Vol. 37, pp. 5464–5471). Washington, DC, United States. <a href=\"https://doi.org/10.1609/aaai.v37i5.25679\">https://doi.org/10.1609/aaai.v37i5.25679</a>","mla":"Avni, Guy, et al. “Bidding Graph Games with Partially-Observable Budgets.” <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>, vol. 37, no. 5, 2023, pp. 5464–71, doi:<a href=\"https://doi.org/10.1609/aaai.v37i5.25679\">10.1609/aaai.v37i5.25679</a>.","ama":"Avni G, Jecker IR, Zikelic D. Bidding graph games with partially-observable budgets. In: <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>. Vol 37. ; 2023:5464-5471. doi:<a href=\"https://doi.org/10.1609/aaai.v37i5.25679\">10.1609/aaai.v37i5.25679</a>","ieee":"G. Avni, I. R. Jecker, and D. Zikelic, “Bidding graph games with partially-observable budgets,” in <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>, Washington, DC, United States, 2023, vol. 37, no. 5, pp. 5464–5471.","short":"G. Avni, I.R. Jecker, D. Zikelic, in:, Proceedings of the 37th AAAI Conference on Artificial Intelligence, 2023, pp. 5464–5471."},"arxiv":1,"month":"06","department":[{"_id":"ToHe"},{"_id":"KrCh"}],"abstract":[{"text":"Two-player zero-sum \"graph games\" are central in logic, verification, and multi-agent systems. The game proceeds by placing a token on a vertex of a graph, and allowing the players to move it to produce an infinite path, which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In \"bidding games\", however, the players have budgets and in each turn, an auction (bidding) determines which player moves the token. So far, bidding games have only been studied as full-information games. In this work we initiate the study of partial-information bidding games: we study bidding games in which a player's initial budget is drawn from a known probability distribution. We show that while for some bidding mechanisms and objectives, it is straightforward to adapt the results from the full-information setting to the partial-information setting, for others, the analysis is significantly more challenging, requires new techniques, and gives rise to interesting results. Specifically, we study games with \"mean-payoff\" objectives in combination with \"poorman\" bidding. We construct optimal strategies for a partially-informed player who plays against a fully-informed adversary. We show that, somewhat surprisingly, the \"value\" under pure strategies does not necessarily exist in such games.","lang":"eng"}],"intvolume":"        37","publication_identifier":{"isbn":["9781577358800"]},"publication_status":"published","title":"Bidding graph games with partially-observable budgets","oa_version":"Published Version","author":[{"first_name":"Guy","orcid":"0000-0001-5588-8287","id":"463C8BC2-F248-11E8-B48F-1D18A9856A87","full_name":"Avni, Guy","last_name":"Avni"},{"id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425","full_name":"Jecker, Ismael R","last_name":"Jecker","first_name":"Ismael R"},{"orcid":"0000-0002-4681-1699","first_name":"Dorde","full_name":"Zikelic, Dorde","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","last_name":"Zikelic"}],"day":"27","scopus_import":"1","date_created":"2023-08-27T22:01:18Z","volume":37,"project":[{"call_identifier":"H2020","grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"}],"status":"public","publication":"Proceedings of the 37th AAAI Conference on Artificial Intelligence","acknowledgement":"This research was supported in part by ISF grant no.1679/21, by the ERC CoG 863818 (ForM-SMArt), and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.","conference":{"location":"Washington, DC, United States","end_date":"2023-02-14","start_date":"2023-02-07","name":"AAAI: Conference on Artificial Intelligence"},"date_published":"2023-06-27T00:00:00Z","ec_funded":1,"external_id":{"arxiv":["2211.13626"]},"year":"2023","page":"5464-5471","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.1609/aaai.v37i5.25679","open_access":"1"}],"doi":"10.1609/aaai.v37i5.25679","article_processing_charge":"No","type":"conference","date_updated":"2025-07-14T09:09:56Z","_id":"14243"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. Complexity of spatial games. In: <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>. Vol 250. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022. doi:<a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11\">10.4230/LIPIcs.FSTTCS.2022.11</a>","short":"K. Chatterjee, R. Ibsen-Jensen, I.R. Jecker, J. Svoboda, in:, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.","ieee":"K. Chatterjee, R. Ibsen-Jensen, I. R. Jecker, and J. Svoboda, “Complexity of spatial games,” in <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, Madras, India, 2022, vol. 250.","chicago":"Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, Ismael R Jecker, and Jakub Svoboda. “Complexity of Spatial Games.” In <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, Vol. 250. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. <a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11\">https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11</a>.","ista":"Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. 2022. Complexity of spatial games. 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. FSTTC: Foundations of Software Technology and Theoretical Computer Science vol. 250, 11:1-11:14.","mla":"Chatterjee, Krishnendu, et al. “Complexity of Spatial Games.” <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, vol. 250, 11:1-11:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, doi:<a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11\">10.4230/LIPIcs.FSTTCS.2022.11</a>.","apa":"Chatterjee, K., Ibsen-Jensen, R., Jecker, I. R., &#38; Svoboda, J. (2022). Complexity of spatial games. In <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i> (Vol. 250). Madras, India: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11\">https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11</a>"},"language":[{"iso":"eng"}],"oa":1,"article_number":"11:1-11:14","file":[{"file_id":"12323","creator":"dernst","date_updated":"2023-01-20T10:19:19Z","file_size":657396,"date_created":"2023-01-20T10:19:19Z","checksum":"a21e3ba2421e2c4a06aa2cb6d530ede1","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_name":"2022_LIPICs_Chatterjee.pdf"}],"department":[{"_id":"KrCh"}],"month":"12","publication_status":"published","publication_identifier":{"isbn":["9783959772617"],"issn":["1868-8969"]},"file_date_updated":"2023-01-20T10:19:19Z","intvolume":"       250","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"text":"Spatial games form a widely-studied class of games from biology and physics modeling the evolution of social behavior. Formally, such a game is defined by a square (d by d) payoff matrix M and an undirected graph G. Each vertex of G represents an individual, that initially follows some strategy i ∈ {1,2,…,d}. In each round of the game, every individual plays the matrix game with each of its neighbors: An individual following strategy i meeting a neighbor following strategy j receives a payoff equal to the entry (i,j) of M. Then, each individual updates its strategy to its neighbors' strategy with the highest sum of payoffs, and the next round starts. The basic computational problems consist of reachability between configurations and the average frequency of a strategy. For general spatial games and graphs, these problems are in PSPACE. In this paper, we examine restricted setting: the game is a prisoner’s dilemma; and G is a subgraph of grid. We prove that basic computational problems for spatial games with prisoner’s dilemma on a subgraph of a grid are PSPACE-hard.","lang":"eng"}],"has_accepted_license":"1","date_created":"2023-01-01T23:00:50Z","volume":250,"title":"Complexity of spatial games","oa_version":"Published Version","author":[{"orcid":"0000-0002-4561-241X","first_name":"Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu"},{"last_name":"Ibsen-Jensen","id":"3B699956-F248-11E8-B48F-1D18A9856A87","full_name":"Ibsen-Jensen, Rasmus","orcid":"0000-0003-4783-0389","first_name":"Rasmus"},{"first_name":"Ismael R","id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425","full_name":"Jecker, Ismael R","last_name":"Jecker"},{"orcid":"0000-0002-1419-3267","first_name":"Jakub","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","full_name":"Svoboda, Jakub","last_name":"Svoboda"}],"scopus_import":"1","day":"14","conference":{"location":"Madras, India","start_date":"2022-12-18","end_date":"2022-12-20","name":"FSTTC: Foundations of Software Technology and Theoretical Computer Science"},"date_published":"2022-12-14T00:00:00Z","acknowledgement":"Krishnendu Chatterjee: The research was partially supported by the ERC CoG 863818\r\n(ForM-SMArt).\r\nIsmaël Jecker: The research was partially supported by the ERC grant 950398 (INFSYS).\r\nJakub Svoboda: The research was partially supported by the ERC CoG 863818 (ForM-SMArt)","ec_funded":1,"project":[{"grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"}],"publication":"42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science","status":"public","year":"2022","quality_controlled":"1","ddc":["000"],"type":"conference","date_updated":"2025-07-14T09:09:55Z","_id":"12101","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","doi":"10.4230/LIPIcs.FSTTCS.2022.11","article_processing_charge":"No"},{"main_file_link":[{"url":"https://arxiv.org/abs/2005.06636","open_access":"1"}],"quality_controlled":"1","page":"617-636","_id":"10694","date_updated":"2025-07-14T09:10:12Z","type":"conference","article_processing_charge":"No","doi":"10.1137/1.9781611976465.38","publisher":"Society for Industrial and Applied Mathematics","editor":[{"first_name":"Dániel","full_name":"Marx, Dániel","last_name":"Marx"}],"ec_funded":1,"date_published":"2021-01-01T00:00:00Z","conference":{"end_date":"2021-01-13","start_date":"2021-01-10","name":"SODA: Symposium on Discrete Algorithms","location":"Virtual"},"acknowledgement":"This research was supported in part by the Austrian Science Fund (FWF) under grant Z211-N23 (Wittgenstein Award), ERC CoG 863818 (FoRM-SMArt), and by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.","publication":"Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms","status":"public","project":[{"_id":"25F42A32-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z211"},{"_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818"},{"name":"International IST Doctoral Program","grant_number":"665385","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"year":"2021","external_id":{"arxiv":["2005.06636"]},"publication_status":"published","publication_identifier":{"isbn":["978-1-61197-646-5"]},"abstract":[{"text":"In a two-player zero-sum graph game the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In bidding games, however, the players have budgets, and in each turn, we hold an “auction” (bidding) to determine which player moves the token: both players simultaneously submit bids and the higher bidder moves the token. The bidding mechanisms differ in their payment schemes. Bidding games were largely studied with variants of first-price bidding in which only the higher bidder pays his bid. We focus on all-pay bidding, where both players pay their bids. Finite-duration all-pay bidding games were studied and shown to be technically more challenging than their first-price counterparts. We study for the first time, infinite-duration all-pay bidding games. Our most interesting results are for mean-payoff objectives: we portray a complete picture for games played on strongly-connected graphs. We study both pure (deterministic) and mixed (probabilistic) strategies and completely characterize the optimal and almost-sure (with probability 1) payoffs the players can respectively guarantee. We show that mean-payoff games under all-pay bidding exhibit the intriguing mathematical properties of their first-price counterparts; namely, an equivalence with random-turn games in which in each turn, the player who moves is selected according to a (biased) coin toss. The equivalences for all-pay bidding are more intricate and unexpected than for first-price bidding.","lang":"eng"}],"date_created":"2022-01-27T12:11:23Z","day":"01","scopus_import":"1","author":[{"full_name":"Avni, Guy","id":"463C8BC2-F248-11E8-B48F-1D18A9856A87","last_name":"Avni","first_name":"Guy","orcid":"0000-0001-5588-8287"},{"first_name":"Ismael R","last_name":"Jecker","full_name":"Jecker, Ismael R","id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425"},{"first_name":"Dorde","orcid":"0000-0002-4681-1699","full_name":"Zikelic, Dorde","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","last_name":"Zikelic"}],"oa_version":"Preprint","title":"Infinite-duration all-pay bidding games","citation":{"short":"G. Avni, I.R. Jecker, D. Zikelic, in:, D. Marx (Ed.), Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2021, pp. 617–636.","ieee":"G. Avni, I. R. Jecker, and D. Zikelic, “Infinite-duration all-pay bidding games,” in <i>Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms</i>, Virtual, 2021, pp. 617–636.","ama":"Avni G, Jecker IR, Zikelic D. Infinite-duration all-pay bidding games. In: Marx D, ed. <i>Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms</i>. Society for Industrial and Applied Mathematics; 2021:617-636. doi:<a href=\"https://doi.org/10.1137/1.9781611976465.38\">10.1137/1.9781611976465.38</a>","mla":"Avni, Guy, et al. “Infinite-Duration All-Pay Bidding Games.” <i>Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms</i>, edited by Dániel Marx, Society for Industrial and Applied Mathematics, 2021, pp. 617–36, doi:<a href=\"https://doi.org/10.1137/1.9781611976465.38\">10.1137/1.9781611976465.38</a>.","apa":"Avni, G., Jecker, I. R., &#38; Zikelic, D. (2021). Infinite-duration all-pay bidding games. In D. Marx (Ed.), <i>Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms</i> (pp. 617–636). Virtual: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611976465.38\">https://doi.org/10.1137/1.9781611976465.38</a>","chicago":"Avni, Guy, Ismael R Jecker, and Dorde Zikelic. “Infinite-Duration All-Pay Bidding Games.” In <i>Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms</i>, edited by Dániel Marx, 617–36. Society for Industrial and Applied Mathematics, 2021. <a href=\"https://doi.org/10.1137/1.9781611976465.38\">https://doi.org/10.1137/1.9781611976465.38</a>.","ista":"Avni G, Jecker IR, Zikelic D. 2021. Infinite-duration all-pay bidding games. Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 617–636."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"GradSch"},{"_id":"KrCh"}],"arxiv":1,"month":"01"},{"type":"conference","date_updated":"2022-05-13T08:12:52Z","_id":"10052","publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","doi":"10.4230/LIPIcs.CONCUR.2021.18","article_processing_charge":"No","alternative_title":["LIPIcs"],"quality_controlled":"1","ddc":["000"],"external_id":{"arxiv":["2107.04683"]},"year":"2021","date_published":"2021-08-13T00:00:00Z","conference":{"location":"Paris, France","name":"CONCUR: Conference on Concurrency Theory","start_date":"2021-08-23","end_date":"2021-08-27"},"acknowledgement":"Ismaël Jecker: Marie Skłodowska-Curie Grant Agreement No. 754411. Nicolas Mazzocchi: BOSCO project PGC2018-102210-B-I00 (MCIU/AEI/FEDER, UE), BLOQUESCM project S2018/TCS-4339, and MINECO grant RYC-2016-20281.\r\nPetra Wolf : DFG project FE 560/9-1.\r\n","ec_funded":1,"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"status":"public","publication":"32nd International Conference on Concurrency Theory","date_created":"2021-09-27T14:33:14Z","volume":203,"title":"Decomposing permutation automata","oa_version":"Published Version","author":[{"full_name":"Jecker, Ismael R","id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425","last_name":"Jecker","first_name":"Ismael R"},{"first_name":"Nicolas","full_name":"Mazzocchi, Nicolas","last_name":"Mazzocchi"},{"full_name":"Wolf, Petra","last_name":"Wolf","first_name":"Petra"}],"day":"13","scopus_import":"1","publication_status":"published","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-9597-7203-7"]},"file_date_updated":"2021-10-01T11:10:53Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"text":"A deterministic finite automaton (DFA) 𝒜 is composite if its language L(𝒜) can be decomposed into an intersection ⋂_{i = 1}^k L(𝒜_i) of languages of smaller DFAs. Otherwise, 𝒜 is prime. This notion of primality was introduced by Kupferman and Mosheiff in 2013, and while they proved that we can decide whether a DFA is composite, the precise complexity of this problem is still open, with a doubly-exponential gap between the upper and lower bounds. In this work, we focus on permutation DFAs, i.e., those for which the transition monoid is a group. We provide an NP algorithm to decide whether a permutation DFA is composite, and show that the difficulty of this problem comes from the number of non-accepting states of the instance: we give a fixed-parameter tractable algorithm with the number of rejecting states as the parameter. Moreover, we investigate the class of commutative permutation DFAs. Their structural properties allow us to decide compositionality in NL, and even in LOGSPACE if the alphabet size is fixed. Despite this low complexity, we show that complex behaviors still arise in this class: we provide a family of composite DFAs each requiring polynomially many factors with respect to its size. We also consider the variant of the problem that asks whether a DFA is k-factor composite, that is, decomposable into k smaller DFAs, for some given integer k ∈ ℕ. We show that, for commutative permutation DFAs, restricting the number of factors makes the decision computationally harder, and yields a problem with tight bounds: it is NP-complete. Finally, we show that in general, this problem is in PSPACE, and it is in LOGSPACE for DFAs with a singleton alphabet.","lang":"eng"}],"intvolume":"       203","has_accepted_license":"1","article_number":"18","file":[{"file_id":"10064","creator":"cchlebak","date_updated":"2021-10-01T11:10:53Z","date_created":"2021-10-01T11:10:53Z","file_size":1003552,"checksum":"4722c81be82265cf45e78adf9db91250","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_name":"2021_CONCUR_Jecker.pdf"}],"department":[{"_id":"KrCh"}],"month":"08","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Jecker IR, Mazzocchi N, Wolf P. Decomposing permutation automata. In: <i>32nd International Conference on Concurrency Theory</i>. Vol 203. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2021.18\">10.4230/LIPIcs.CONCUR.2021.18</a>","short":"I.R. Jecker, N. Mazzocchi, P. Wolf, in:, 32nd International Conference on Concurrency Theory, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.","ieee":"I. R. Jecker, N. Mazzocchi, and P. Wolf, “Decomposing permutation automata,” in <i>32nd International Conference on Concurrency Theory</i>, Paris, France, 2021, vol. 203.","ista":"Jecker IR, Mazzocchi N, Wolf P. 2021. Decomposing permutation automata. 32nd International Conference on Concurrency Theory. CONCUR: Conference on Concurrency Theory, LIPIcs, vol. 203, 18.","chicago":"Jecker, Ismael R, Nicolas Mazzocchi, and Petra Wolf. “Decomposing Permutation Automata.” In <i>32nd International Conference on Concurrency Theory</i>, Vol. 203. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2021.18\">https://doi.org/10.4230/LIPIcs.CONCUR.2021.18</a>.","mla":"Jecker, Ismael R., et al. “Decomposing Permutation Automata.” <i>32nd International Conference on Concurrency Theory</i>, vol. 203, 18, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2021.18\">10.4230/LIPIcs.CONCUR.2021.18</a>.","apa":"Jecker, I. R., Mazzocchi, N., &#38; Wolf, P. (2021). Decomposing permutation automata. In <i>32nd International Conference on Concurrency Theory</i> (Vol. 203). Paris, France: Schloss Dagstuhl - Leibniz Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2021.18\">https://doi.org/10.4230/LIPIcs.CONCUR.2021.18</a>"},"language":[{"iso":"eng"}],"oa":1},{"language":[{"iso":"eng"}],"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Jecker, I. R. (2021). A Ramsey theorem for finite monoids. In <i>38th International Symposium on Theoretical Aspects of Computer Science</i> (Vol. 187). Saarbrücken, Germany: Schloss Dagstuhl - Leibniz Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.STACS.2021.44\">https://doi.org/10.4230/LIPIcs.STACS.2021.44</a>","mla":"Jecker, Ismael R. “A Ramsey Theorem for Finite Monoids.” <i>38th International Symposium on Theoretical Aspects of Computer Science</i>, vol. 187, 44, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.STACS.2021.44\">10.4230/LIPIcs.STACS.2021.44</a>.","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.","chicago":"Jecker, Ismael R. “A Ramsey Theorem for Finite Monoids.” In <i>38th International Symposium on Theoretical Aspects of Computer Science</i>, Vol. 187. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.STACS.2021.44\">https://doi.org/10.4230/LIPIcs.STACS.2021.44</a>.","ieee":"I. R. Jecker, “A Ramsey theorem for finite monoids,” in <i>38th International Symposium on Theoretical Aspects of Computer Science</i>, Saarbrücken, Germany, 2021, vol. 187.","short":"I.R. Jecker, in:, 38th International Symposium on Theoretical Aspects of Computer Science, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.","ama":"Jecker IR. A Ramsey theorem for finite monoids. In: <i>38th International Symposium on Theoretical Aspects of Computer Science</i>. Vol 187. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.STACS.2021.44\">10.4230/LIPIcs.STACS.2021.44</a>"},"month":"03","file":[{"relation":"main_file","checksum":"17432a05733f408de300e17e390a90e4","file_name":"2021_LIPIcs_Jecker.pdf","success":1,"content_type":"application/pdf","access_level":"open_access","file_id":"10063","file_size":720250,"date_created":"2021-10-01T09:55:00Z","date_updated":"2021-10-01T09:55:00Z","creator":"cchlebak"}],"article_number":"44","department":[{"_id":"KrCh"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"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 𝒟-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 𝒟-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 𝒟-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 𝒟-length of (n²+n+2)/2.","lang":"eng"}],"intvolume":"       187","has_accepted_license":"1","file_date_updated":"2021-10-01T09:55:00Z","publication_status":"published","publication_identifier":{"isbn":["978-3-9597-7180-1"],"issn":["1868-8969"]},"title":"A Ramsey theorem for finite monoids","oa_version":"Published Version","scopus_import":"1","day":"10","author":[{"last_name":"Jecker","full_name":"Jecker, Ismael R","id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425","first_name":"Ismael R"}],"date_created":"2021-09-27T14:33:15Z","volume":187,"status":"public","publication":"38th International Symposium on Theoretical Aspects of Computer Science","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"date_published":"2021-03-10T00:00:00Z","conference":{"location":"Saarbrücken, Germany","name":"STACS: Symposium on Theoretical Aspects of Computer Science","start_date":"2021-03-16","end_date":"2021-03-19"},"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.","ec_funded":1,"external_id":{"isi":["000635691700044"]},"isi":1,"year":"2021","ddc":["000"],"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","article_processing_charge":"No","alternative_title":["LIPIcs"],"doi":"10.4230/LIPIcs.STACS.2021.44","type":"conference","_id":"10055","date_updated":"2023-08-14T07:03:23Z"},{"file_date_updated":"2021-10-06T12:44:05Z","publication_identifier":{"isbn":["978-3-9597-7201-3"],"issn":["1868-8969"]},"publication_status":"published","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"text":"We study the expressiveness and succinctness of good-for-games pushdown automata (GFG-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of the remainder of the input word. We prove that GFG-PDA recognise more languages than deterministic PDA (DPDA) but not all context-free languages (CFL). This class is orthogonal to unambiguous CFL. We further show that GFG-PDA can be exponentially more succinct than DPDA, while PDA can be double-exponentially more succinct than GFG-PDA. We also study GFGness in visibly pushdown automata (VPA), which enjoy better closure properties than PDA, and for which we show GFGness to be ExpTime-complete. GFG-VPA can be exponentially more succinct than deterministic VPA, while VPA can be exponentially more succinct than GFG-VPA. Both of these lower bounds are tight. Finally, we study the complexity of resolving nondeterminism in GFG-PDA. Every GFG-PDA has a positional resolver, a function that resolves nondeterminism and that is only dependant on the current configuration. Pushdown transducers are sufficient to implement the resolvers of GFG-VPA, but not those of GFG-PDA. GFG-PDA with finite-state resolvers are determinisable.","lang":"eng"}],"intvolume":"       202","volume":202,"date_created":"2021-10-03T22:01:23Z","scopus_import":"1","day":"18","author":[{"first_name":"Shibashis","full_name":"Guha, Shibashis","last_name":"Guha"},{"first_name":"Ismael R","full_name":"Jecker, Ismael R","id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425","last_name":"Jecker"},{"first_name":"Karoliina","full_name":"Lehtinen, Karoliina","last_name":"Lehtinen"},{"full_name":"Zimmermann, Martin","last_name":"Zimmermann","first_name":"Martin"}],"title":"A bit of nondeterminism makes pushdown automata expressive and succinct","oa_version":"Published Version","citation":{"short":"S. Guha, I.R. Jecker, K. Lehtinen, M. Zimmermann, in:, 46th International Symposium on Mathematical Foundations of Computer Science, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.","ieee":"S. Guha, I. R. Jecker, K. Lehtinen, and M. Zimmermann, “A bit of nondeterminism makes pushdown automata expressive and succinct,” in <i>46th International Symposium on Mathematical Foundations of Computer Science</i>, Tallinn, Estonia, 2021, vol. 202.","ama":"Guha S, Jecker IR, Lehtinen K, Zimmermann M. A bit of nondeterminism makes pushdown automata expressive and succinct. In: <i>46th International Symposium on Mathematical Foundations of Computer Science</i>. Vol 202. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2021.53\">10.4230/LIPIcs.MFCS.2021.53</a>","mla":"Guha, Shibashis, et al. “A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct.” <i>46th International Symposium on Mathematical Foundations of Computer Science</i>, vol. 202, 53, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2021.53\">10.4230/LIPIcs.MFCS.2021.53</a>.","apa":"Guha, S., Jecker, I. R., Lehtinen, K., &#38; Zimmermann, M. (2021). A bit of nondeterminism makes pushdown automata expressive and succinct. In <i>46th International Symposium on Mathematical Foundations of Computer Science</i> (Vol. 202). Tallinn, Estonia: Schloss Dagstuhl - Leibniz Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2021.53\">https://doi.org/10.4230/LIPIcs.MFCS.2021.53</a>","chicago":"Guha, Shibashis, Ismael R Jecker, Karoliina Lehtinen, and Martin Zimmermann. “A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct.” In <i>46th International Symposium on Mathematical Foundations of Computer Science</i>, Vol. 202. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2021.53\">https://doi.org/10.4230/LIPIcs.MFCS.2021.53</a>.","ista":"Guha S, Jecker IR, Lehtinen K, Zimmermann M. 2021. A bit of nondeterminism makes pushdown automata expressive and succinct. 46th International Symposium on Mathematical Foundations of Computer Science. MFCS: Mathematical Foundations of Computer Science, LIPIcs, vol. 202, 53."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"KrCh"}],"file":[{"success":1,"file_name":"2021_LIPIcs_Guha.pdf","access_level":"open_access","content_type":"application/pdf","relation":"main_file","checksum":"f4d407d43a97330c3fb11e6a7a6fbfb2","date_created":"2021-10-06T12:44:05Z","file_size":825567,"creator":"cchlebak","date_updated":"2021-10-06T12:44:05Z","file_id":"10097"}],"article_number":"53","month":"08","arxiv":1,"quality_controlled":"1","ddc":["000"],"_id":"10075","date_updated":"2022-05-13T08:21:56Z","type":"conference","article_processing_charge":"No","alternative_title":["LIPIcs"],"doi":"10.4230/LIPIcs.MFCS.2021.53","publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","ec_funded":1,"date_published":"2021-08-18T00:00:00Z","conference":{"location":"Tallinn, Estonia","end_date":"2021-08-27","start_date":"2021-08-23","name":"MFCS: Mathematical Foundations of Computer Science"},"acknowledgement":"Ismaël Jecker: Funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 754411. Karoliina Lehtinen: Funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 892704.","publication":"46th International Symposium on Mathematical Foundations of Computer Science","status":"public","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"year":"2021","external_id":{"arxiv":["2105.02611"]}},{"external_id":{"arxiv":["2110.01279"]},"year":"2021","publication":"41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science","status":"public","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"conference":{"location":"Virtual","end_date":"2021-12-17","start_date":"2021-12-15","name":"FSTTCS: Foundations of Software Technology and Theoretical Computer Science"},"date_published":"2021-11-29T00:00:00Z","acknowledgement":"We like to thank Lukas Fleischer and Michael Wehar for our discussions. This work started at the Schloss Dagstuhl Event 20483 Moderne Aspekte der Komplexitätstheorie in der Automatentheorie https://www.dagstuhl.de/20483.\r\n","ec_funded":1,"publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","alternative_title":["LIPIcs"],"article_processing_charge":"No","doi":"10.4230/LIPIcs.FSTTCS.2021.34","type":"conference","_id":"10630","date_updated":"2022-01-17T10:56:19Z","ddc":["000"],"quality_controlled":"1","arxiv":1,"month":"11","article_number":"34","file":[{"relation":"main_file","checksum":"d5a82ba893c3bc5da5914edbb3efb92b","success":1,"file_name":"2021_LIPIcs_Arrighi.pdf","access_level":"open_access","content_type":"application/pdf","file_id":"10634","file_size":844224,"date_created":"2022-01-17T10:49:03Z","date_updated":"2022-01-17T10:49:03Z","creator":"cchlebak"}],"department":[{"_id":"KrCh"}],"language":[{"iso":"eng"}],"oa":1,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"ama":"Arrighi E, Fernau H, Hoffmann S, et al. On the complexity of intersection non-emptiness for star-free language classes. In: <i>41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>. Vol 213. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34\">10.4230/LIPIcs.FSTTCS.2021.34</a>","ieee":"E. Arrighi <i>et al.</i>, “On the complexity of intersection non-emptiness for star-free language classes,” in <i>41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, Virtual, 2021, vol. 213.","short":"E. Arrighi, H. Fernau, S. Hoffmann, M. Holzer, I.R. Jecker, M. De Oliveira Oliveira, P. Wolf, in:, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.","ista":"Arrighi E, Fernau H, Hoffmann S, Holzer M, Jecker IR, De Oliveira Oliveira M, Wolf P. 2021. On the complexity of intersection non-emptiness for star-free language classes. 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. FSTTCS: Foundations of Software Technology and Theoretical Computer Science, LIPIcs, vol. 213, 34.","chicago":"Arrighi, Emmanuel, Henning Fernau, Stefan Hoffmann, Markus Holzer, Ismael R Jecker, Mateus De Oliveira Oliveira, and Petra Wolf. “On the Complexity of Intersection Non-Emptiness for Star-Free Language Classes.” In <i>41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, Vol. 213. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34\">https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34</a>.","apa":"Arrighi, E., Fernau, H., Hoffmann, S., Holzer, M., Jecker, I. R., De Oliveira Oliveira, M., &#38; Wolf, P. (2021). On the complexity of intersection non-emptiness for star-free language classes. In <i>41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i> (Vol. 213). Virtual: Schloss Dagstuhl - Leibniz Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34\">https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34</a>","mla":"Arrighi, Emmanuel, et al. “On the Complexity of Intersection Non-Emptiness for Star-Free Language Classes.” <i>41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, vol. 213, 34, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34\">10.4230/LIPIcs.FSTTCS.2021.34</a>."},"title":"On the complexity of intersection non-emptiness for star-free language classes","oa_version":"Published Version","scopus_import":"1","day":"29","author":[{"first_name":"Emmanuel","last_name":"Arrighi","full_name":"Arrighi, Emmanuel"},{"full_name":"Fernau, Henning","last_name":"Fernau","first_name":"Henning"},{"first_name":"Stefan","last_name":"Hoffmann","full_name":"Hoffmann, Stefan"},{"first_name":"Markus","full_name":"Holzer, Markus","last_name":"Holzer"},{"last_name":"Jecker","full_name":"Jecker, Ismael R","id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425","first_name":"Ismael R"},{"first_name":"Mateus","full_name":"De Oliveira Oliveira, Mateus","last_name":"De Oliveira Oliveira"},{"first_name":"Petra","last_name":"Wolf","full_name":"Wolf, Petra"}],"date_created":"2022-01-16T23:01:29Z","volume":213,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"       213","abstract":[{"text":"In the Intersection Non-emptiness problem, we are given a list of finite automata A_1, A_2,… , A_m over a common alphabet Σ as input, and the goal is to determine whether some string w ∈ Σ^* lies in the intersection of the languages accepted by the automata in the list. We analyze the complexity of the Intersection Non-emptiness problem under the promise that all input automata accept a language in some level of the dot-depth hierarchy, or some level of the Straubing-Thérien hierarchy. Automata accepting languages from the lowest levels of these hierarchies arise naturally in the context of model checking. We identify a dichotomy in the dot-depth hierarchy by showing that the problem is already NP-complete when all input automata accept languages of the levels B_0 or B_{1/2} and already PSPACE-hard when all automata accept a language from the level B_1. Conversely, we identify a tetrachotomy in the Straubing-Thérien hierarchy. More precisely, we show that the problem is in AC^0 when restricted to level L_0; complete for L or NL, depending on the input representation, when restricted to languages in the level L_{1/2}; NP-complete when the input is given as DFAs accepting a language in L_1 or L_{3/2}; and finally, PSPACE-complete when the input automata accept languages in level L_2 or higher. Moreover, we show that the proof technique used to show containment in NP for DFAs accepting languages in L_1 or L_{3/2} does not generalize to the context of NFAs. To prove this, we identify a family of languages that provide an exponential separation between the state complexity of general NFAs and that of partially ordered NFAs. To the best of our knowledge, this is the first superpolynomial separation between these two models of computation.","lang":"eng"}],"has_accepted_license":"1","file_date_updated":"2022-01-17T10:49:03Z","publication_status":"published","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-9597-7215-0"]}},{"article_processing_charge":"No","alternative_title":["LIPIcs"],"doi":"10.4230/LIPIcs.MFCS.2020.22","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","_id":"8533","date_updated":"2025-06-02T08:53:42Z","type":"conference","ddc":["000"],"quality_controlled":"1","year":"2020","external_id":{"arxiv":["2007.02894"]},"status":"public","publication":"45th International Symposium on Mathematical Foundations of Computer Science","project":[{"_id":"25892FC0-B435-11E9-9278-68D0E5697425","name":"Efficient Algorithms for Computer Aided Verification","grant_number":"ICT15-003"},{"call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"date_published":"2020-08-18T00:00:00Z","conference":{"name":"MFCS: Symposium on Mathematical Foundations of Computer Science","start_date":"2020-08-24","end_date":"2020-08-28","location":"Prague, Czech Republic"},"acknowledgement":"Krishnendu Chatterjee: The research was partially supported by the Vienna Science and\r\nTechnology Fund (WWTF) Project ICT15-003.\r\nIsmaël Jecker: This project has received funding from the European Union’s Horizon 2020 research\r\nand innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","scopus_import":"1","day":"18","author":[{"orcid":"0000-0002-4561-241X","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee"},{"orcid":"0000-0003-4783-0389","first_name":"Rasmus","full_name":"Ibsen-Jensen, Rasmus","id":"3B699956-F248-11E8-B48F-1D18A9856A87","last_name":"Ibsen-Jensen"},{"first_name":"Ismael R","full_name":"Jecker, Ismael R","id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425","last_name":"Jecker"},{"id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","full_name":"Svoboda, Jakub","last_name":"Svoboda","first_name":"Jakub","orcid":"0000-0002-1419-3267"}],"title":"Simplified game of life: Algorithms and complexity","oa_version":"Published Version","volume":170,"date_created":"2020-09-20T22:01:36Z","has_accepted_license":"1","license":"https://creativecommons.org/licenses/by/3.0/","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","image":"/images/cc_by.png","short":"CC BY (3.0)"},"intvolume":"       170","abstract":[{"lang":"eng","text":"Game of Life is a simple and elegant model to study dynamical system over networks. The model consists of a graph where every vertex has one of two types, namely, dead or alive. A configuration is a mapping of the vertices to the types. An update rule describes how the type of a vertex is updated given the types of its neighbors. In every round, all vertices are updated synchronously, which leads to a configuration update. While in general, Game of Life allows a broad range of update rules, we focus on two simple families of update rules, namely, underpopulation and overpopulation, that model several interesting dynamics studied in the literature. In both settings, a dead vertex requires at least a desired number of live neighbors to become alive. For underpopulation (resp., overpopulation), a live vertex requires at least (resp. at most) a desired number of live neighbors to remain alive. We study the basic computation problems, e.g., configuration reachability, for these two families of rules. For underpopulation rules, we show that these problems can be solved in polynomial time, whereas for overpopulation rules they are PSPACE-complete."}],"file_date_updated":"2020-09-21T13:57:34Z","publication_identifier":{"issn":["18688969"],"isbn":["9783959771597"]},"publication_status":"published","arxiv":1,"month":"08","department":[{"_id":"KrCh"}],"article_number":"22:1-22:13","file":[{"checksum":"bbd7c4f55d45f2ff2a0a4ef0e10a77b1","relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_name":"2020_LIPIcs_Chatterjee.pdf","success":1,"file_id":"8550","date_updated":"2020-09-21T13:57:34Z","creator":"dernst","file_size":491374,"date_created":"2020-09-21T13:57:34Z"}],"oa":1,"language":[{"iso":"eng"}],"citation":{"ama":"Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. Simplified game of life: Algorithms and complexity. In: <i>45th International Symposium on Mathematical Foundations of Computer Science</i>. Vol 170. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2020.22\">10.4230/LIPIcs.MFCS.2020.22</a>","ieee":"K. Chatterjee, R. Ibsen-Jensen, I. R. Jecker, and J. Svoboda, “Simplified game of life: Algorithms and complexity,” in <i>45th International Symposium on Mathematical Foundations of Computer Science</i>, Prague, Czech Republic, 2020, vol. 170.","short":"K. Chatterjee, R. Ibsen-Jensen, I.R. Jecker, J. Svoboda, in:, 45th International Symposium on Mathematical Foundations of Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","chicago":"Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, Ismael R Jecker, and Jakub Svoboda. “Simplified Game of Life: Algorithms and Complexity.” In <i>45th International Symposium on Mathematical Foundations of Computer Science</i>, Vol. 170. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2020.22\">https://doi.org/10.4230/LIPIcs.MFCS.2020.22</a>.","ista":"Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. 2020. Simplified game of life: Algorithms and complexity. 45th International Symposium on Mathematical Foundations of Computer Science. MFCS: Symposium on Mathematical Foundations of Computer Science, LIPIcs, vol. 170, 22:1-22:13.","apa":"Chatterjee, K., Ibsen-Jensen, R., Jecker, I. R., &#38; Svoboda, J. (2020). Simplified game of life: Algorithms and complexity. In <i>45th International Symposium on Mathematical Foundations of Computer Science</i> (Vol. 170). Prague, Czech Republic: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2020.22\">https://doi.org/10.4230/LIPIcs.MFCS.2020.22</a>","mla":"Chatterjee, Krishnendu, et al. “Simplified Game of Life: Algorithms and Complexity.” <i>45th International Symposium on Mathematical Foundations of Computer Science</i>, vol. 170, 22:1-22:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2020.22\">10.4230/LIPIcs.MFCS.2020.22</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"month":"08","article_number":"51:1-51:12","file":[{"relation":"main_file","checksum":"2dc9e2fad6becd4563aef3e27a473f70","success":1,"file_name":"2020_LIPIcsMFCS_Jecker.pdf","access_level":"open_access","content_type":"application/pdf","file_id":"8552","file_size":597977,"date_created":"2020-09-21T14:17:08Z","creator":"dernst","date_updated":"2020-09-21T14:17:08Z"}],"department":[{"_id":"KrCh"}],"language":[{"iso":"eng"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Jecker IR, Kupferman O, Mazzocchi N. Unary prime languages. In: <i>45th International Symposium on Mathematical Foundations of Computer Science</i>. Vol 170. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2020.51\">10.4230/LIPIcs.MFCS.2020.51</a>","short":"I.R. Jecker, O. Kupferman, N. Mazzocchi, in:, 45th International Symposium on Mathematical Foundations of Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","ieee":"I. R. Jecker, O. Kupferman, and N. Mazzocchi, “Unary prime languages,” in <i>45th International Symposium on Mathematical Foundations of Computer Science</i>, Prague, Czech Republic, 2020, vol. 170.","ista":"Jecker IR, Kupferman O, Mazzocchi N. 2020. Unary prime languages. 45th International Symposium on Mathematical Foundations of Computer Science. MFCS: Symposium on Mathematical Foundations of Computer Science, LIPIcs, vol. 170, 51:1-51:12.","chicago":"Jecker, Ismael R, Orna Kupferman, and Nicolas Mazzocchi. “Unary Prime Languages.” In <i>45th International Symposium on Mathematical Foundations of Computer Science</i>, Vol. 170. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2020.51\">https://doi.org/10.4230/LIPIcs.MFCS.2020.51</a>.","mla":"Jecker, Ismael R., et al. “Unary Prime Languages.” <i>45th International Symposium on Mathematical Foundations of Computer Science</i>, vol. 170, 51:1-51:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2020.51\">10.4230/LIPIcs.MFCS.2020.51</a>.","apa":"Jecker, I. R., Kupferman, O., &#38; Mazzocchi, N. (2020). Unary prime languages. In <i>45th International Symposium on Mathematical Foundations of Computer Science</i> (Vol. 170). Prague, Czech Republic: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2020.51\">https://doi.org/10.4230/LIPIcs.MFCS.2020.51</a>"},"oa_version":"Published Version","title":"Unary prime languages","author":[{"first_name":"Ismael R","full_name":"Jecker, Ismael R","id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425","last_name":"Jecker"},{"first_name":"Orna","last_name":"Kupferman","full_name":"Kupferman, Orna"},{"full_name":"Mazzocchi, Nicolas","last_name":"Mazzocchi","first_name":"Nicolas"}],"day":"18","scopus_import":"1","date_created":"2020-09-20T22:01:36Z","volume":170,"intvolume":"       170","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","image":"/images/cc_by.png","short":"CC BY (3.0)"},"abstract":[{"lang":"eng","text":"A regular language L of finite words is composite if there are regular languages L₁,L₂,…,L_t such that L = ⋂_{i = 1}^t L_i and the index (number of states in a minimal DFA) of every language L_i is strictly smaller than the index of L. Otherwise, L is prime. Primality of regular languages was introduced and studied in [O. Kupferman and J. Mosheiff, 2015], where the complexity of deciding the primality of the language of a given DFA was left open, with a doubly-exponential gap between the upper and lower bounds. We study primality for unary regular languages, namely regular languages with a singleton alphabet. A unary language corresponds to a subset of ℕ, making the study of unary prime languages closer to that of primality in number theory. We show that the setting of languages is richer. In particular, while every composite number is the product of two smaller numbers, the number t of languages necessary to decompose a composite unary language induces a strict hierarchy. In addition, a primality witness for a unary language L, namely a word that is not in L but is in all products of languages that contain L and have an index smaller than L’s, may be of exponential length. Still, we are able to characterize compositionality by structural properties of a DFA for L, leading to a LogSpace algorithm for primality checking of unary DFAs."}],"has_accepted_license":"1","publication_status":"published","publication_identifier":{"isbn":["9783959771597"],"issn":["18688969"]},"file_date_updated":"2020-09-21T14:17:08Z","year":"2020","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020"}],"publication":"45th International Symposium on Mathematical Foundations of Computer Science","status":"public","date_published":"2020-08-18T00:00:00Z","acknowledgement":"Ismaël Jecker: This project has received funding from the European Union’s Horizon\r\n2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No.\r\n754411. Nicolas Mazzocchi: PhD fellowship FRIA from the F.R.S.-FNRS.","conference":{"location":"Prague, Czech Republic","end_date":"2020-08-28","start_date":"2020-08-24","name":"MFCS: Symposium on Mathematical Foundations of Computer Science"},"ec_funded":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","doi":"10.4230/LIPIcs.MFCS.2020.51","article_processing_charge":"No","alternative_title":["LIPIcs"],"type":"conference","date_updated":"2021-01-12T08:19:56Z","_id":"8534","ddc":["000"],"quality_controlled":"1"}]