--- _id: '475' abstract: - lang: eng text: 'First cycle games (FCG) are played on a finite graph by two players who push a token along the edges until a vertex is repeated, and a simple cycle is formed. The winner is determined by some fixed property Y of the sequence of labels of the edges (or nodes) forming this cycle. These games are traditionally of interest because of their connection with infinite-duration games such as parity and mean-payoff games. We study the memory requirements for winning strategies of FCGs and certain associated infinite duration games. We exhibit a simple FCG that is not memoryless determined (this corrects a mistake in Memoryless determinacy of parity and mean payoff games: a simple proof by Bj⋯orklund, Sandberg, Vorobyov (2004) that claims that FCGs for which Y is closed under cyclic permutations are memoryless determined). We show that θ (n)! memory (where n is the number of nodes in the graph), which is always sufficient, may be necessary to win some FCGs. On the other hand, we identify easy to check conditions on Y (i.e., Y is closed under cyclic permutations, and both Y and its complement are closed under concatenation) that are sufficient to ensure that the corresponding FCGs and their associated infinite duration games are memoryless determined. We demonstrate that many games considered in the literature, such as mean-payoff, parity, energy, etc., satisfy these conditions. On the complexity side, we show (for efficiently computable Y) that while solving FCGs is in PSPACE, solving some families of FCGs is PSPACE-hard. ' alternative_title: - EPTCS author: - first_name: Benjamin full_name: Aminof, Benjamin id: 4A55BD00-F248-11E8-B48F-1D18A9856A87 last_name: Aminof - first_name: Sasha full_name: Rubin, Sasha id: 2EC51194-F248-11E8-B48F-1D18A9856A87 last_name: Rubin citation: ama: 'Aminof B, Rubin S. First cycle games. In: Electronic Proceedings in Theoretical Computer Science, EPTCS. Vol 146. Open Publishing Association; 2014:83-90. doi:10.4204/EPTCS.146.11' apa: 'Aminof, B., & Rubin, S. (2014). First cycle games. In Electronic Proceedings in Theoretical Computer Science, EPTCS (Vol. 146, pp. 83–90). Grenoble, France: Open Publishing Association. https://doi.org/10.4204/EPTCS.146.11' chicago: Aminof, Benjamin, and Sasha Rubin. “First Cycle Games.” In Electronic Proceedings in Theoretical Computer Science, EPTCS, 146:83–90. Open Publishing Association, 2014. https://doi.org/10.4204/EPTCS.146.11. ieee: B. Aminof and S. Rubin, “First cycle games,” in Electronic Proceedings in Theoretical Computer Science, EPTCS, Grenoble, France, 2014, vol. 146, pp. 83–90. ista: 'Aminof B, Rubin S. 2014. First cycle games. Electronic Proceedings in Theoretical Computer Science, EPTCS. SR: Strategic Reasoning, EPTCS, vol. 146, 83–90.' mla: Aminof, Benjamin, and Sasha Rubin. “First Cycle Games.” Electronic Proceedings in Theoretical Computer Science, EPTCS, vol. 146, Open Publishing Association, 2014, pp. 83–90, doi:10.4204/EPTCS.146.11. short: B. Aminof, S. Rubin, in:, Electronic Proceedings in Theoretical Computer Science, EPTCS, Open Publishing Association, 2014, pp. 83–90. conference: end_date: 2014-04-06 location: Grenoble, France name: 'SR: Strategic Reasoning' start_date: 2014-04-05 date_created: 2018-12-11T11:46:41Z date_published: 2014-04-01T00:00:00Z date_updated: 2021-01-12T08:00:53Z day: '01' ddc: - '004' department: - _id: KrCh doi: 10.4204/EPTCS.146.11 ec_funded: 1 file: - access_level: open_access checksum: 4d7b4ab82980cca2b96ac7703992a8c8 content_type: application/pdf creator: system date_created: 2018-12-12T10:17:08Z date_updated: 2020-07-14T12:46:35Z file_id: '5260' file_name: IST-2018-952-v1+1_2014_Rubin_First_cycle.pdf file_size: 100115 relation: main_file file_date_updated: 2020-07-14T12:46:35Z has_accepted_license: '1' intvolume: ' 146' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 83 - 90 project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25F5A88A-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11402-N23 name: Moderne Concurrency Paradigms - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 25892FC0-B435-11E9-9278-68D0E5697425 grant_number: ICT15-003 name: Efficient Algorithms for Computer Aided Verification publication: Electronic Proceedings in Theoretical Computer Science, EPTCS publication_status: published publisher: Open Publishing Association publist_id: '7345' pubrep_id: '952' quality_controlled: '1' scopus_import: 1 status: public title: First cycle 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: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 146 year: '2014' ...