--- _id: '6752' abstract: - lang: eng text: 'Two-player games on graphs are widely studied in formal methods, as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several common modes to determine how the players move the token through the graph; e.g., in turn-based games the players alternate turns in moving the token. We study the bidding mode of moving the token, which, to the best of our knowledge, has never been studied in infinite-duration games. The following bidding rule was previously defined and called Richman bidding. Both players have separate budgets, which sum up to 1. In each turn, a bidding takes place: Both players submit bids simultaneously, where a bid is legal if it does not exceed the available budget, and the higher bidder pays his bid to the other player and moves the token. The central question studied in bidding games is a necessary and sufficient initial budget for winning the game: a threshold budget in a vertex is a value t ∈ [0, 1] such that if Player 1’s budget exceeds t, he can win the game; and if Player 2’s budget exceeds 1 − t, he can win the game. Threshold budgets were previously shown to exist in every vertex of a reachability game, which have an interesting connection with random-turn games—a sub-class of simple stochastic games in which the player who moves is chosen randomly. We show the existence of threshold budgets for a qualitative class of infinite-duration games, namely parity games, and a quantitative class, namely mean-payoff games. The key component of the proof is a quantitative solution to strongly connected mean-payoff bidding games in which we extend the connection with random-turn games to these games, and construct explicit optimal strategies for both players.' article_number: '31' article_processing_charge: No author: - first_name: Guy full_name: Avni, Guy id: 463C8BC2-F248-11E8-B48F-1D18A9856A87 last_name: Avni orcid: 0000-0001-5588-8287 - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000−0002−2985−7724 - first_name: Ventsislav K full_name: Chonev, Ventsislav K id: 36CBE2E6-F248-11E8-B48F-1D18A9856A87 last_name: Chonev citation: ama: Avni G, Henzinger TA, Chonev VK. Infinite-duration bidding games. Journal of the ACM. 2019;66(4). doi:10.1145/3340295 apa: Avni, G., Henzinger, T. A., & Chonev, V. K. (2019). Infinite-duration bidding games. Journal of the ACM. ACM. https://doi.org/10.1145/3340295 chicago: Avni, Guy, Thomas A Henzinger, and Ventsislav K Chonev. “Infinite-Duration Bidding Games.” Journal of the ACM. ACM, 2019. https://doi.org/10.1145/3340295. ieee: G. Avni, T. A. Henzinger, and V. K. Chonev, “Infinite-duration bidding games,” Journal of the ACM, vol. 66, no. 4. ACM, 2019. ista: Avni G, Henzinger TA, Chonev VK. 2019. Infinite-duration bidding games. Journal of the ACM. 66(4), 31. mla: Avni, Guy, et al. “Infinite-Duration Bidding Games.” Journal of the ACM, vol. 66, no. 4, 31, ACM, 2019, doi:10.1145/3340295. short: G. Avni, T.A. Henzinger, V.K. Chonev, Journal of the ACM 66 (2019). date_created: 2019-08-04T21:59:16Z date_published: 2019-07-16T00:00:00Z date_updated: 2023-08-29T07:02:13Z day: '16' department: - _id: ToHe doi: 10.1145/3340295 external_id: arxiv: - '1705.01433' isi: - '000487714900008' intvolume: ' 66' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1705.01433 month: '07' oa: 1 oa_version: Preprint project: - _id: 25F42A32-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z211 name: The Wittgenstein Prize - _id: 25F2ACDE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11402-N23 name: Rigorous Systems Engineering - _id: 264B3912-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02369 name: Formal Methods meets Algorithmic Game Theory publication: Journal of the ACM publication_identifier: eissn: - 1557735X issn: - '00045411' publication_status: published publisher: ACM quality_controlled: '1' related_material: record: - id: '950' relation: earlier_version status: public scopus_import: '1' status: public title: Infinite-duration bidding games type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 66 year: '2019' ... --- _id: '950' abstract: - lang: eng text: "Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several common modes to determine how the players move the token through the graph; e.g., in turn-based games the players alternate turns in moving the token. We study the bidding mode of moving the token, which, to the best of our knowledge, has never been studied in infinite-duration games. Both players have separate budgets, which sum up to $1$. In each turn, a bidding takes place. Both players submit bids simultaneously, and a bid is legal if it does not exceed the available budget. The winner of the bidding pays his bid to the other player and moves the token. For reachability objectives, repeated bidding games have been studied and are called Richman games. There, a central question is the existence and computation of threshold budgets; namely, a value t\\in [0,1] such that if\\PO's budget exceeds $t$, he can win the game, and if\\PT's budget exceeds 1-t, he can win the game. We focus on parity games and mean-payoff games. We show the existence of threshold budgets in these games, and reduce the problem of finding them to Richman games. We also determine the strategy-complexity of an optimal strategy. Our most interesting result shows that memoryless strategies suffice for mean-payoff bidding games. \r\n" alternative_title: - LIPIcs article_number: '17' author: - first_name: Guy full_name: Avni, Guy id: 463C8BC2-F248-11E8-B48F-1D18A9856A87 last_name: Avni orcid: 0000-0001-5588-8287 - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000−0002−2985−7724 - first_name: Ventsislav K full_name: Chonev, Ventsislav K id: 36CBE2E6-F248-11E8-B48F-1D18A9856A87 last_name: Chonev citation: ama: 'Avni G, Henzinger TA, Chonev VK. Infinite-duration bidding games. In: Vol 85. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017. doi:10.4230/LIPIcs.CONCUR.2017.21' apa: 'Avni, G., Henzinger, T. A., & Chonev, V. K. (2017). Infinite-duration bidding games (Vol. 85). Presented at the CONCUR: Concurrency Theory, Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.CONCUR.2017.21' chicago: Avni, Guy, Thomas A Henzinger, and Ventsislav K Chonev. “Infinite-Duration Bidding Games,” Vol. 85. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.CONCUR.2017.21. ieee: 'G. Avni, T. A. Henzinger, and V. K. Chonev, “Infinite-duration bidding games,” presented at the CONCUR: Concurrency Theory, Berlin, Germany, 2017, vol. 85.' ista: 'Avni G, Henzinger TA, Chonev VK. 2017. Infinite-duration bidding games. CONCUR: Concurrency Theory, LIPIcs, vol. 85, 17.' mla: Avni, Guy, et al. Infinite-Duration Bidding Games. Vol. 85, 17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, doi:10.4230/LIPIcs.CONCUR.2017.21. short: G. Avni, T.A. Henzinger, V.K. Chonev, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. conference: end_date: 2017-09-07 location: Berlin, Germany name: 'CONCUR: Concurrency Theory' start_date: 2017-09-05 date_created: 2018-12-11T11:49:22Z date_published: 2017-09-01T00:00:00Z date_updated: 2023-08-29T07:02:13Z day: '01' ddc: - '000' department: - _id: ToHe - _id: KrCh doi: 10.4230/LIPIcs.CONCUR.2017.21 external_id: arxiv: - '1705.01433' file: - access_level: open_access checksum: 6d5cccf755207b91ccbef95d8275b013 content_type: application/pdf creator: system date_created: 2018-12-12T10:18:00Z date_updated: 2020-07-14T12:48:16Z file_id: '5318' file_name: IST-2017-844-v1+1_concur-cr.pdf file_size: 335170 relation: main_file file_date_updated: 2020-07-14T12:48:16Z has_accepted_license: '1' intvolume: ' 85' language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 25F42A32-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z211 name: The Wittgenstein Prize publication_identifier: issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '6466' pubrep_id: '844' quality_controlled: '1' related_material: record: - id: '6752' relation: later_version status: public scopus_import: 1 status: public title: Infinite-duration bidding games 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 85 year: '2017' ... --- _id: '1069' abstract: - lang: eng text: "The Continuous Skolem Problem asks whether a real-valued function satisfying a linear differen-\r\ntial equation has a zero in a given interval of real numbers. This is a fundamental reachability\r\nproblem for continuous linear dynamical systems, such as linear hybrid automata and continuous-\r\ntime Markov chains. Decidability of the problem is currently open – indeed decidability is open\r\neven for the sub-problem in which a zero is sought in a bounded interval. In this paper we show\r\ndecidability of the bounded problem subject to Schanuel’s Conjecture, a unifying conjecture in\r\ntranscendental number theory. We furthermore analyse the unbounded problem in terms of the\r\nfrequencies of the differential equation, that is, the imaginary parts of the characteristic roots.\r\nWe show that the unbounded problem can be reduced to the bounded problem if there is at most\r\none rationally linearly independent frequency, or if there are two rationally linearly independent\r\nfrequencies and all characteristic roots are simple. We complete the picture by showing that de-\r\ncidability of the unbounded problem in the case of two (or more) rationally linearly independent\r\nfrequencies would entail a major new effectiveness result in Diophantine approximation, namely\r\ncomputability of the Diophantine-approximation types of all real algebraic numbers." acknowledgement: 'Ventsislav Chonev is supported by Austrian Science Fund (FWF) NFN Grant No S11407-N23 (RiSE/SHiNE), ERC Start grant (279307: Graph Games), and ERC Advanced Grant (267989: QUAREM).' alternative_title: - LIPIcs article_number: '100' author: - first_name: Ventsislav K full_name: Chonev, Ventsislav K id: 36CBE2E6-F248-11E8-B48F-1D18A9856A87 last_name: Chonev - first_name: Joël full_name: Ouaknine, Joël last_name: Ouaknine - first_name: James full_name: Worrell, James last_name: Worrell citation: ama: 'Chonev VK, Ouaknine J, Worrell J. On the skolem problem for continuous linear dynamical systems. In: Vol 55. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik; 2016. doi:10.4230/LIPIcs.ICALP.2016.100' apa: 'Chonev, V. K., Ouaknine, J., & Worrell, J. (2016). On the skolem problem for continuous linear dynamical systems (Vol. 55). Presented at the ICALP: Automata, Languages and Programming, Rome, Italy: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2016.100' chicago: Chonev, Ventsislav K, Joël Ouaknine, and James Worrell. “On the Skolem Problem for Continuous Linear Dynamical Systems,” Vol. 55. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik, 2016. https://doi.org/10.4230/LIPIcs.ICALP.2016.100. ieee: 'V. K. Chonev, J. Ouaknine, and J. Worrell, “On the skolem problem for continuous linear dynamical systems,” presented at the ICALP: Automata, Languages and Programming, Rome, Italy, 2016, vol. 55.' ista: 'Chonev VK, Ouaknine J, Worrell J. 2016. On the skolem problem for continuous linear dynamical systems. ICALP: Automata, Languages and Programming, LIPIcs, vol. 55, 100.' mla: Chonev, Ventsislav K., et al. On the Skolem Problem for Continuous Linear Dynamical Systems. Vol. 55, 100, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik, 2016, doi:10.4230/LIPIcs.ICALP.2016.100. short: V.K. Chonev, J. Ouaknine, J. Worrell, in:, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik, 2016. conference: end_date: 2016-07-15 location: Rome, Italy name: 'ICALP: Automata, Languages and Programming' start_date: 2016-07-12 date_created: 2018-12-11T11:49:59Z date_published: 2016-08-01T00:00:00Z date_updated: 2021-01-12T06:48:03Z day: '01' ddc: - '004' - '006' department: - _id: KrCh doi: 10.4230/LIPIcs.ICALP.2016.100 ec_funded: 1 file: - access_level: open_access content_type: application/pdf creator: system date_created: 2018-12-12T10:16:26Z date_updated: 2018-12-12T10:16:26Z file_id: '5213' file_name: IST-2017-778-v1+1_LIPIcs-ICALP-2016-100.pdf file_size: 521415 relation: main_file file_date_updated: 2018-12-12T10:16:26Z has_accepted_license: '1' intvolume: ' 55' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 25EE3708-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '267989' name: Quantitative Reactive Modeling publication_status: published publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik publist_id: '6314' pubrep_id: '778' quality_controlled: '1' scopus_import: 1 status: public title: On the skolem problem for continuous linear dynamical systems 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 55 year: '2016' ... --- _id: '1380' abstract: - lang: eng text: We consider higher-dimensional versions of Kannan and Lipton's Orbit Problem - determining whether a target vector space V may be reached from a starting point x under repeated applications of a linear transformation A. Answering two questions posed by Kannan and Lipton in the 1980s, we show that when V has dimension one, this problem is solvable in polynomial time, and when V has dimension two or three, the problem is in NPRP. article_number: '23' author: - first_name: Ventsislav K full_name: Chonev, Ventsislav K id: 36CBE2E6-F248-11E8-B48F-1D18A9856A87 last_name: Chonev - first_name: Joël full_name: Ouaknine, Joël last_name: Ouaknine - first_name: James full_name: Worrell, James last_name: Worrell citation: ama: Chonev VK, Ouaknine J, Worrell J. On the complexity of the orbit problem. Journal of the ACM. 2016;63(3). doi:10.1145/2857050 apa: Chonev, V. K., Ouaknine, J., & Worrell, J. (2016). On the complexity of the orbit problem. Journal of the ACM. ACM. https://doi.org/10.1145/2857050 chicago: Chonev, Ventsislav K, Joël Ouaknine, and James Worrell. “On the Complexity of the Orbit Problem.” Journal of the ACM. ACM, 2016. https://doi.org/10.1145/2857050. ieee: V. K. Chonev, J. Ouaknine, and J. Worrell, “On the complexity of the orbit problem,” Journal of the ACM, vol. 63, no. 3. ACM, 2016. ista: Chonev VK, Ouaknine J, Worrell J. 2016. On the complexity of the orbit problem. Journal of the ACM. 63(3), 23. mla: Chonev, Ventsislav K., et al. “On the Complexity of the Orbit Problem.” Journal of the ACM, vol. 63, no. 3, 23, ACM, 2016, doi:10.1145/2857050. short: V.K. Chonev, J. Ouaknine, J. Worrell, Journal of the ACM 63 (2016). date_created: 2018-12-11T11:51:41Z date_published: 2016-06-01T00:00:00Z date_updated: 2021-01-12T06:50:17Z day: '01' department: - _id: KrCh doi: 10.1145/2857050 intvolume: ' 63' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1303.2981 month: '06' oa: 1 oa_version: Preprint publication: Journal of the ACM publication_status: published publisher: ACM publist_id: '5831' quality_controlled: '1' scopus_import: 1 status: public title: On the complexity of the orbit problem type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 63 year: '2016' ... --- _id: '1389' abstract: - lang: eng text: "The continuous evolution of a wide variety of systems, including continous-time Markov chains and linear hybrid automata, can be\r\ndescribed in terms of linear differential equations. In this paper we study the decision problem of whether the solution x(t) of a system of linear differential equations dx/dt = Ax reaches a target halfspace infinitely often. This recurrent reachability problem can\r\nequivalently be formulated as the following Infinite Zeros Problem: does a real-valued function f:R≥0 --> R satisfying a given linear\r\ndifferential equation have infinitely many zeros? Our main decidability result is that if the differential equation has order at most 7, then the Infinite Zeros Problem is decidable. On the other hand, we show that a decision procedure for the Infinite Zeros Problem at order 9 (and above) would entail a major breakthrough in Diophantine Approximation, specifically an algorithm for computing the Lagrange constants of arbitrary real algebraic numbers to arbitrary precision." author: - first_name: Ventsislav K full_name: Chonev, Ventsislav K id: 36CBE2E6-F248-11E8-B48F-1D18A9856A87 last_name: Chonev - first_name: Joël full_name: Ouaknine, Joël last_name: Ouaknine - first_name: James full_name: Worrell, James last_name: Worrell citation: ama: 'Chonev VK, Ouaknine J, Worrell J. On recurrent reachability for continuous linear dynamical systems. In: LICS ’16. IEEE; 2016:515-524. doi:10.1145/2933575.2934548' apa: 'Chonev, V. K., Ouaknine, J., & Worrell, J. (2016). On recurrent reachability for continuous linear dynamical systems. In LICS ’16 (pp. 515–524). New York, NY, USA: IEEE. https://doi.org/10.1145/2933575.2934548' chicago: Chonev, Ventsislav K, Joël Ouaknine, and James Worrell. “On Recurrent Reachability for Continuous Linear Dynamical Systems.” In LICS ’16, 515–24. IEEE, 2016. https://doi.org/10.1145/2933575.2934548. ieee: V. K. Chonev, J. Ouaknine, and J. Worrell, “On recurrent reachability for continuous linear dynamical systems,” in LICS ’16, New York, NY, USA, 2016, pp. 515–524. ista: 'Chonev VK, Ouaknine J, Worrell J. 2016. On recurrent reachability for continuous linear dynamical systems. LICS ’16. LICS: Logic in Computer Science, 515–524.' mla: Chonev, Ventsislav K., et al. “On Recurrent Reachability for Continuous Linear Dynamical Systems.” LICS ’16, IEEE, 2016, pp. 515–24, doi:10.1145/2933575.2934548. short: V.K. Chonev, J. Ouaknine, J. Worrell, in:, LICS ’16, IEEE, 2016, pp. 515–524. conference: end_date: 2018-07-08 location: New York, NY, USA name: 'LICS: Logic in Computer Science' start_date: 2018-07-05 date_created: 2018-12-11T11:51:44Z date_published: 2016-07-05T00:00:00Z date_updated: 2021-01-12T06:50:20Z day: '05' department: - _id: KrCh doi: 10.1145/2933575.2934548 ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1507.03632 month: '07' oa: 1 oa_version: Preprint page: 515 - 524 project: - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 25EE3708-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '267989' name: Quantitative Reactive Modeling publication: LICS '16 publication_status: published publisher: IEEE publist_id: '5820' quality_controlled: '1' scopus_import: 1 status: public title: On recurrent reachability for continuous linear dynamical systems type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2016' ...