--- _id: '497' abstract: - lang: eng text: 'One central issue in the formal design and analysis of reactive systems is the notion of refinement that asks whether all behaviors of the implementation is allowed by the specification. The local interpretation of behavior leads to the notion of simulation. Alternating transition systems (ATSs) provide a general model for composite reactive systems, and the simulation relation for ATSs is known as alternating simulation. The simulation relation for fair transition systems is called fair simulation. In this work our main contributions are as follows: (1) We present an improved algorithm for fair simulation with Büchi fairness constraints; our algorithm requires O(n 3·m) time as compared to the previous known O(n 6)-time algorithm, where n is the number of states and m is the number of transitions. (2) We present a game based algorithm for alternating simulation that requires O(m2)-time as compared to the previous known O((n·m)2)-time algorithm, where n is the number of states and m is the size of transition relation. (3) We present an iterative algorithm for alternating simulation that matches the time complexity of the game based algorithm, but is more space efficient than the game based algorithm. © Krishnendu Chatterjee, Siddhesh Chaubal, and Pritish Kamath.' alternative_title: - LIPIcs author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Siddhesh full_name: Chaubal, Siddhesh last_name: Chaubal - first_name: Pritish full_name: Kamath, Pritish last_name: Kamath citation: ama: 'Chatterjee K, Chaubal S, Kamath P. Faster algorithms for alternating refinement relations. In: Vol 16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2012:167-182. doi:10.4230/LIPIcs.CSL.2012.167' apa: 'Chatterjee, K., Chaubal, S., & Kamath, P. (2012). Faster algorithms for alternating refinement relations (Vol. 16, pp. 167–182). Presented at the EACSL: European Association for Computer Science Logic, Fontainebleau, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.CSL.2012.167' chicago: Chatterjee, Krishnendu, Siddhesh Chaubal, and Pritish Kamath. “Faster Algorithms for Alternating Refinement Relations,” 16:167–82. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012. https://doi.org/10.4230/LIPIcs.CSL.2012.167. ieee: 'K. Chatterjee, S. Chaubal, and P. Kamath, “Faster algorithms for alternating refinement relations,” presented at the EACSL: European Association for Computer Science Logic, Fontainebleau, France, 2012, vol. 16, pp. 167–182.' ista: 'Chatterjee K, Chaubal S, Kamath P. 2012. Faster algorithms for alternating refinement relations. EACSL: European Association for Computer Science Logic, LIPIcs, vol. 16, 167–182.' mla: Chatterjee, Krishnendu, et al. Faster Algorithms for Alternating Refinement Relations. Vol. 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012, pp. 167–82, doi:10.4230/LIPIcs.CSL.2012.167. short: K. Chatterjee, S. Chaubal, P. Kamath, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012, pp. 167–182. conference: end_date: 2012-09-06 location: Fontainebleau, France name: 'EACSL: European Association for Computer Science Logic' start_date: 2012-09-03 date_created: 2018-12-11T11:46:48Z date_published: 2012-09-01T00:00:00Z date_updated: 2023-02-23T12:23:32Z day: '01' ddc: - '004' department: - _id: KrCh doi: 10.4230/LIPIcs.CSL.2012.167 ec_funded: 1 file: - access_level: open_access checksum: f1b0dd99240800db2d7dbf9b5131fe5e content_type: application/pdf creator: system date_created: 2018-12-12T10:08:50Z date_updated: 2020-07-14T12:46:35Z file_id: '4712' file_name: IST-2018-943-v1+1_2012_Chatterjee_Faster_Algorithms.pdf file_size: 471236 relation: main_file file_date_updated: 2020-07-14T12:46:35Z has_accepted_license: '1' intvolume: ' 16' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 167 - 182 project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _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: 2587B514-B435-11E9-9278-68D0E5697425 name: Microsoft Research Faculty Fellowship publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '7323' pubrep_id: '943' quality_controlled: '1' related_material: record: - id: '5378' relation: earlier_version status: public scopus_import: 1 status: public title: Faster algorithms for alternating refinement relations tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2012' ... --- _id: '3165' abstract: - lang: eng text: Computing the winning set for Büchi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications. The long standing best known upper bound for solving the problem is Õ(n·m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the Õ(n·m) boundary by presenting a new technique that reduces the running time to O(n 2). This bound also leads to O(n 2) time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of Õ(n·m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n 3)), and (3) in Markov decision processes (improving for m > n 4/3 an earlier bound of O(min(m 1.5, m·n 2/3)). We also show that the same technique can be used to compute the maximal end-component decomposition of a graph in time O(n 2), which is an improvement over earlier bounds for m > n 4/3. Finally, we show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. This is the first dynamic algorithm for this problem. acknowledgement: 'The research was supported by Austrian Science Fund (FWF) Grant No P 23499-N23 on Modern Graph Algorithmic Techniques in Formal Verification, Vienna Science and Technology Fund (WWTF) Grant ICT10-002, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.' 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: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 citation: ama: 'Chatterjee K, Henzinger MH. An O(n2) time algorithm for alternating Büchi games. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM; 2012:1386-1399. doi:10.1137/1.9781611973099.109' apa: 'Chatterjee, K., & Henzinger, M. H. (2012). An O(n2) time algorithm for alternating Büchi games. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 1386–1399). Kyoto, Japan: SIAM. https://doi.org/10.1137/1.9781611973099.109' chicago: Chatterjee, Krishnendu, and Monika H Henzinger. “An O(N2) Time Algorithm for Alternating Büchi Games.” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 1386–99. SIAM, 2012. https://doi.org/10.1137/1.9781611973099.109. ieee: K. Chatterjee and M. H. Henzinger, “An O(n2) time algorithm for alternating Büchi games,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Kyoto, Japan, 2012, pp. 1386–1399. ista: 'Chatterjee K, Henzinger MH. 2012. An O(n2) time algorithm for alternating Büchi games. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 1386–1399.' mla: Chatterjee, Krishnendu, and Monika H. Henzinger. “An O(N2) Time Algorithm for Alternating Büchi Games.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2012, pp. 1386–99, doi:10.1137/1.9781611973099.109. short: K. Chatterjee, M.H. Henzinger, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2012, pp. 1386–1399. conference: end_date: 2012-01-19 location: Kyoto, Japan name: 'SODA: Symposium on Discrete Algorithms' start_date: 2012-01-17 date_created: 2018-12-11T12:01:46Z date_published: 2012-01-01T00:00:00Z date_updated: 2023-02-23T12:23:35Z day: '01' department: - _id: KrCh doi: 10.1137/1.9781611973099.109 ec_funded: 1 external_id: arxiv: - '1109.5018' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1109.5018 month: '01' oa: 1 oa_version: None page: 1386 - 1399 project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _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: 2587B514-B435-11E9-9278-68D0E5697425 name: Microsoft Research Faculty Fellowship publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms publication_status: published publisher: SIAM publist_id: '3519' pubrep_id: '15' quality_controlled: '1' related_material: record: - id: '2141' relation: later_version status: public - id: '5379' relation: earlier_version status: public status: public title: An O(n2) time algorithm for alternating Büchi games type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '2956' abstract: - lang: eng text: 'Two-player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can model the control flow of sequential programs with recursion. While pushdown games have been studied before with qualitative objectives, such as reachability and parity objectives, in this work we study for the first time such games with the most well-studied quantitative objective, namely, mean payoff objectives. In pushdown games two types of strategies are relevant: (1) global strategies, that depend on the entire global history; and (2) modular strategies, that have only local memory and thus do not depend on the context of invocation, but only on the history of the current invocation of the module. Our main results are as follows: (1) One-player pushdown games with mean-payoff objectives under global strategies are decidable in polynomial time. (2) Two-player pushdown games with mean-payoff objectives under global strategies are undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies are NP-hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies are NP-complete). We also establish the optimal strategy complexity showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games; and memoryless modular strategies are sufficient in two-player pushdown games. Finally we also show that all the problems have the same computational complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.' acknowledgement: "The research was supported by Austrian Science Fund (FWF) Grant No P 23499-N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), Microsoft faculty fellows award, the Israeli Centers of Research Excellence (ICORE) program, (Center No. 4/11), the RICH Model Toolkit (ICT COST Action IC0901), and was carried out in partial fulfillment of the requirements for the Ph.D. degree of the second author.\r\nA Technical Report of this paper is available via internal link." article_number: '6280438' author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Yaron full_name: Velner, Yaron last_name: Velner citation: ama: 'Chatterjee K, Velner Y. Mean payoff pushdown games. In: Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. IEEE; 2012. doi:10.1109/LICS.2012.30' apa: 'Chatterjee, K., & Velner, Y. (2012). Mean payoff pushdown games. In Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. Dubrovnik, Croatia : IEEE. https://doi.org/10.1109/LICS.2012.30' chicago: Chatterjee, Krishnendu, and Yaron Velner. “Mean Payoff Pushdown Games.” In Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. IEEE, 2012. https://doi.org/10.1109/LICS.2012.30. ieee: K. Chatterjee and Y. Velner, “Mean payoff pushdown games,” in Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, Dubrovnik, Croatia , 2012. ista: 'Chatterjee K, Velner Y. 2012. Mean payoff pushdown games. Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Logic in Computer Science, 6280438.' mla: Chatterjee, Krishnendu, and Yaron Velner. “Mean Payoff Pushdown Games.” Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, 6280438, IEEE, 2012, doi:10.1109/LICS.2012.30. short: K. Chatterjee, Y. Velner, in:, Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, IEEE, 2012. conference: end_date: 2012-06-28 location: 'Dubrovnik, Croatia ' name: 'LICS: Logic in Computer Science' start_date: 2012-06-25 date_created: 2018-12-11T12:00:32Z date_published: 2012-08-23T00:00:00Z date_updated: 2023-02-23T12:23:30Z day: '23' department: - _id: KrCh doi: 10.1109/LICS.2012.30 ec_funded: 1 language: - iso: eng month: '08' oa_version: None project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _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: 2587B514-B435-11E9-9278-68D0E5697425 name: Microsoft Research Faculty Fellowship publication: Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science publication_status: published publisher: IEEE publist_id: '3770' quality_controlled: '1' related_material: record: - id: '5377' relation: earlier_version status: public scopus_import: 1 status: public title: Mean payoff pushdown games type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '5377' abstract: - lang: eng text: 'Two-player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can model the control flow of sequential programs with recursion. While pushdown games have been studied before with qualitative objectives, such as reachability and ω-regular objectives, in this work we study for the first time such games with the most well-studied quantitative objective, namely, mean-payoff objectives. In pushdown games two types of strategies are relevant: (1) global strategies, that depend on the entire global history; and (2) modular strategies, that have only local memory and thus do not depend on the context of invocation, but only on the history of the current invocation of the module. Our main results are as follows: (1) One-player pushdown games with mean-payoff objectives under global strategies are decidable in polynomial time. (2) Two- player pushdown games with mean-payoff objectives under global strategies are undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies are NP- hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies are NP-complete). We also establish the optimal strategy complexity showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games; and memoryless modular strategies are sufficient in two- player pushdown games. Finally we also show that all the problems have the same complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.' alternative_title: - IST Austria Technical Report author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Yaron full_name: Velner, Yaron last_name: Velner citation: ama: Chatterjee K, Velner Y. Mean-Payoff Pushdown Games. IST Austria; 2012. doi:10.15479/AT:IST-2012-0002 apa: Chatterjee, K., & Velner, Y. (2012). Mean-payoff pushdown games. IST Austria. https://doi.org/10.15479/AT:IST-2012-0002 chicago: Chatterjee, Krishnendu, and Yaron Velner. Mean-Payoff Pushdown Games. IST Austria, 2012. https://doi.org/10.15479/AT:IST-2012-0002. ieee: K. Chatterjee and Y. Velner, Mean-payoff pushdown games. IST Austria, 2012. ista: Chatterjee K, Velner Y. 2012. Mean-payoff pushdown games, IST Austria, 33p. mla: Chatterjee, Krishnendu, and Yaron Velner. Mean-Payoff Pushdown Games. IST Austria, 2012, doi:10.15479/AT:IST-2012-0002. short: K. Chatterjee, Y. Velner, Mean-Payoff Pushdown Games, IST Austria, 2012. date_created: 2018-12-12T11:38:59Z date_published: 2012-07-02T00:00:00Z date_updated: 2023-02-23T11:05:50Z day: '02' ddc: - '000' - '005' department: - _id: KrCh doi: 10.15479/AT:IST-2012-0002 file: - access_level: open_access checksum: a03c08c1589dbb0c96183a8bcf3ab240 content_type: application/pdf creator: system date_created: 2018-12-12T11:54:00Z date_updated: 2020-07-14T12:46:38Z file_id: '5522' file_name: IST-2012-002_IST-2012-0002.pdf file_size: 592098 relation: main_file file_date_updated: 2020-07-14T12:46:38Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '33' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '10' related_material: record: - id: '2956' relation: later_version status: public status: public title: Mean-payoff pushdown games type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '5378' abstract: - lang: eng text: 'One central issue in the formal design and analysis of reactive systems is the notion of refinement that asks whether all behaviors of the implementation is allowed by the specification. The local interpretation of behavior leads to the notion of simulation. Alternating transition systems (ATSs) provide a general model for composite reactive systems, and the simulation relation for ATSs is known as alternating simulation. The simulation relation for fair transition systems is called fair simulation. In this work our main contributions are as follows: (1) We present an improved algorithm for fair simulation with Büchi fairness constraints; our algorithm requires O(n3 · m) time as compared to the previous known O(n6)-time algorithm, where n is the number of states and m is the number of transitions. (2) We present a game based algorithm for alternating simulation that requires O(m2)-time as compared to the previous known O((n · m)2)-time algorithm, where n is the number of states and m is the size of transition relation. (3) We present an iterative algorithm for alternating simulation that matches the time complexity of the game based algorithm, but is more space efficient than the game based algorithm.' alternative_title: - IST Austria Technical Report author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Siddhesh full_name: Chaubal, Siddhesh last_name: Chaubal - first_name: Pritish full_name: Kamath, Pritish last_name: Kamath citation: ama: Chatterjee K, Chaubal S, Kamath P. Faster Algorithms for Alternating Refinement Relations. IST Austria; 2012. doi:10.15479/AT:IST-2012-0001 apa: Chatterjee, K., Chaubal, S., & Kamath, P. (2012). Faster algorithms for alternating refinement relations. IST Austria. https://doi.org/10.15479/AT:IST-2012-0001 chicago: Chatterjee, Krishnendu, Siddhesh Chaubal, and Pritish Kamath. Faster Algorithms for Alternating Refinement Relations. IST Austria, 2012. https://doi.org/10.15479/AT:IST-2012-0001. ieee: K. Chatterjee, S. Chaubal, and P. Kamath, Faster algorithms for alternating refinement relations. IST Austria, 2012. ista: Chatterjee K, Chaubal S, Kamath P. 2012. Faster algorithms for alternating refinement relations, IST Austria, 21p. mla: Chatterjee, Krishnendu, et al. Faster Algorithms for Alternating Refinement Relations. IST Austria, 2012, doi:10.15479/AT:IST-2012-0001. short: K. Chatterjee, S. Chaubal, P. Kamath, Faster Algorithms for Alternating Refinement Relations, IST Austria, 2012. date_created: 2018-12-12T11:38:59Z date_published: 2012-07-04T00:00:00Z date_updated: 2023-02-23T12:21:38Z day: '04' ddc: - '000' - '005' department: - _id: KrCh doi: 10.15479/AT:IST-2012-0001 file: - access_level: open_access checksum: ec8d1857cc7095d3de5107a0162ced37 content_type: application/pdf creator: system date_created: 2018-12-12T11:53:28Z date_updated: 2020-07-14T12:46:39Z file_id: '5489' file_name: IST-2012-0001_IST-2012-0001.pdf file_size: 394256 relation: main_file file_date_updated: 2020-07-14T12:46:39Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '21' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '14' related_material: record: - id: '497' relation: later_version status: public status: public title: Faster algorithms for alternating refinement relations type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2012' ...