--- _id: '5419' abstract: - lang: eng text: "We consider the reachability and shortest path problems on low tree-width graphs, with n nodes, m edges, and tree-width t, on a standard RAM with wordsize W. We use O to hide polynomial factors of the inverse of the Ackermann function. Our main contributions are three fold:\r\n1. For reachability, we present an algorithm that requires O(n·t2·log(n/t)) preprocessing time, O(n·(t·log(n/t))/W) space, and O(t/W) time for pair queries and O((n·t)/W) time for single-source queries. Note that for constant t our algorithm uses O(n·logn) time for preprocessing; and O(n/W) time for single-source queries, which is faster than depth first search/breath first search (after the preprocessing).\r\n2. We present an algorithm for shortest path that requires O(n·t2) preprocessing time, O(n·t) space, and O(t2) time for pair queries and O(n·t) time single-source queries.\r\n3. We give a space versus query time trade-off algorithm for shortest path that, given any constant >0, requires O(n·t2) preprocessing time, O(n·t2) space, and O(n1−·t2) time for pair queries.\r\nOur algorithms improve all existing results, and use very simple data structures." 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: Rasmus full_name: Ibsen-Jensen, Rasmus id: 3B699956-F248-11E8-B48F-1D18A9856A87 last_name: Ibsen-Jensen orcid: 0000-0003-4783-0389 - first_name: Andreas full_name: Pavlogiannis, Andreas id: 49704004-F248-11E8-B48F-1D18A9856A87 last_name: Pavlogiannis orcid: 0000-0002-8943-0722 citation: ama: Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs. IST Austria; 2014. doi:10.15479/AT:IST-2014-187-v1-1 apa: Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2014). Improved algorithms for reachability and shortest path on low tree-width graphs. IST Austria. https://doi.org/10.15479/AT:IST-2014-187-v1-1 chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs. IST Austria, 2014. https://doi.org/10.15479/AT:IST-2014-187-v1-1. ieee: K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, Improved algorithms for reachability and shortest path on low tree-width graphs. IST Austria, 2014. ista: Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2014. Improved algorithms for reachability and shortest path on low tree-width graphs, IST Austria, 34p. mla: Chatterjee, Krishnendu, et al. Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs. IST Austria, 2014, doi:10.15479/AT:IST-2014-187-v1-1. short: K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs, IST Austria, 2014. date_created: 2018-12-12T11:39:13Z date_published: 2014-04-14T00:00:00Z date_updated: 2021-01-12T08:02:03Z day: '14' ddc: - '000' department: - _id: KrCh doi: 10.15479/AT:IST-2014-187-v1-1 file: - access_level: open_access checksum: c608e66030a4bf51d2d99b451f539b99 content_type: application/pdf creator: system date_created: 2018-12-12T11:54:25Z date_updated: 2020-07-14T12:46:50Z file_id: '5548' file_name: IST-2014-187-v1+1_main_full_tech.pdf file_size: 670031 relation: main_file file_date_updated: 2020-07-14T12:46:50Z has_accepted_license: '1' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: '34' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '187' status: public title: Improved algorithms for reachability and shortest path on low tree-width graphs type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '5418' abstract: - lang: eng text: We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a decidability result for partial-observation games where the first and third player are in a coalition against the second player, thus where the second player is adversarial but weaker due to partial-observation. We establish tight complexity bounds in the case where player 1 is less informed than player 2, namely 2-EXPTIME-completeness for parity objectives. The symmetric case of player 1 more informed than player 2 is much more complicated, and we show that already in the case where player 1 has perfect observation, memory of size non-elementary is necessary in general for reachability objectives, and the problem is decidable for safety and reachability objectives. Our results have tight connections with partial-observation stochastic games for which we derive new complexity results. 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: Laurent full_name: Doyen, Laurent last_name: Doyen citation: ama: Chatterjee K, Doyen L. Games with a Weak Adversary. IST Austria; 2014. doi:10.15479/AT:IST-2014-176-v1-1 apa: Chatterjee, K., & Doyen, L. (2014). Games with a weak adversary. IST Austria. https://doi.org/10.15479/AT:IST-2014-176-v1-1 chicago: Chatterjee, Krishnendu, and Laurent Doyen. Games with a Weak Adversary. IST Austria, 2014. https://doi.org/10.15479/AT:IST-2014-176-v1-1. ieee: K. Chatterjee and L. Doyen, Games with a weak adversary. IST Austria, 2014. ista: Chatterjee K, Doyen L. 2014. Games with a weak adversary, IST Austria, 18p. mla: Chatterjee, Krishnendu, and Laurent Doyen. Games with a Weak Adversary. IST Austria, 2014, doi:10.15479/AT:IST-2014-176-v1-1. short: K. Chatterjee, L. Doyen, Games with a Weak Adversary, IST Austria, 2014. date_created: 2018-12-12T11:39:13Z date_published: 2014-03-22T00:00:00Z date_updated: 2023-02-23T10:30:58Z day: '22' ddc: - '000' - '005' department: - _id: KrCh doi: 10.15479/AT:IST-2014-176-v1-1 file: - access_level: open_access checksum: 1d6958aa60050e1c3e932c6e5f34c39f content_type: application/pdf creator: system date_created: 2018-12-12T11:53:07Z date_updated: 2020-07-14T12:46:49Z file_id: '5468' file_name: IST-2014-176-v1+1_icalp_14.pdf file_size: 328253 relation: main_file file_date_updated: 2020-07-14T12:46:49Z has_accepted_license: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: '18' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '176' related_material: record: - id: '2163' relation: later_version status: public status: public title: Games with a weak adversary type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '5420' abstract: - lang: eng text: 'We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the long-run average of the rewards. The value is the maximal expected payoff that player 1 can guarantee against all strategies of player 2. We consider the computation of the set of states with value 1 under finite-memory strategies for player 1, and our main results for the problem are as follows: (1) we present a polynomial-time algorithm; (2) we show that whenever there is a finite-memory strategy, there is a stationary strategy that does not need memory at all; and (3) we present an optimal bound (which is double exponential) on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy).' 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: Rasmus full_name: Ibsen-Jensen, Rasmus id: 3B699956-F248-11E8-B48F-1D18A9856A87 last_name: Ibsen-Jensen orcid: 0000-0003-4783-0389 citation: ama: Chatterjee K, Ibsen-Jensen R. The Value 1 Problem for Concurrent Mean-Payoff Games. IST Austria; 2014. doi:10.15479/AT:IST-2014-191-v1-1 apa: Chatterjee, K., & Ibsen-Jensen, R. (2014). The value 1 problem for concurrent mean-payoff games. IST Austria. https://doi.org/10.15479/AT:IST-2014-191-v1-1 chicago: Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. The Value 1 Problem for Concurrent Mean-Payoff Games. IST Austria, 2014. https://doi.org/10.15479/AT:IST-2014-191-v1-1. ieee: K. Chatterjee and R. Ibsen-Jensen, The value 1 problem for concurrent mean-payoff games. IST Austria, 2014. ista: Chatterjee K, Ibsen-Jensen R. 2014. The value 1 problem for concurrent mean-payoff games, IST Austria, 49p. mla: Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. The Value 1 Problem for Concurrent Mean-Payoff Games. IST Austria, 2014, doi:10.15479/AT:IST-2014-191-v1-1. short: K. Chatterjee, R. Ibsen-Jensen, The Value 1 Problem for Concurrent Mean-Payoff Games, IST Austria, 2014. date_created: 2018-12-12T11:39:14Z date_published: 2014-04-14T00:00:00Z date_updated: 2021-01-12T08:02:05Z day: '14' ddc: - '000' - '005' department: - _id: KrCh doi: 10.15479/AT:IST-2014-191-v1-1 file: - access_level: open_access checksum: 49e0fd3e62650346daf7dc04604f7a0a content_type: application/pdf creator: system date_created: 2018-12-12T11:53:58Z date_updated: 2020-07-14T12:46:50Z file_id: '5520' file_name: IST-2014-191-v1+1_main_full.pdf file_size: 584368 relation: main_file file_date_updated: 2020-07-14T12:46:50Z has_accepted_license: '1' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: '49' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '191' status: public title: The value 1 problem for concurrent mean-payoff games type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '5424' abstract: - lang: eng text: We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty. 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: Martin full_name: Chmelik, Martin id: 3624234E-F248-11E8-B48F-1D18A9856A87 last_name: Chmelik - first_name: Raghav full_name: Gupta, Raghav last_name: Gupta - first_name: Ayush full_name: Kanodia, Ayush last_name: Kanodia citation: ama: Chatterjee K, Chmelik M, Gupta R, Kanodia A. Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications. IST Austria; 2014. doi:10.15479/AT:IST-2014-305-v1-1 apa: Chatterjee, K., Chmelik, M., Gupta, R., & Kanodia, A. (2014). Qualitative analysis of POMDPs with temporal logic specifications for robotics applications. IST Austria. https://doi.org/10.15479/AT:IST-2014-305-v1-1 chicago: Chatterjee, Krishnendu, Martin Chmelik, Raghav Gupta, and Ayush Kanodia. Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications. IST Austria, 2014. https://doi.org/10.15479/AT:IST-2014-305-v1-1. ieee: K. Chatterjee, M. Chmelik, R. Gupta, and A. Kanodia, Qualitative analysis of POMDPs with temporal logic specifications for robotics applications. IST Austria, 2014. ista: Chatterjee K, Chmelik M, Gupta R, Kanodia A. 2014. Qualitative analysis of POMDPs with temporal logic specifications for robotics applications, IST Austria, 12p. mla: Chatterjee, Krishnendu, et al. Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications. IST Austria, 2014, doi:10.15479/AT:IST-2014-305-v1-1. short: K. Chatterjee, M. Chmelik, R. Gupta, A. Kanodia, Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications, IST Austria, 2014. date_created: 2018-12-12T11:39:15Z date_published: 2014-09-09T00:00:00Z date_updated: 2023-02-23T12:25:52Z day: '09' ddc: - '005' department: - _id: KrCh doi: 10.15479/AT:IST-2014-305-v1-1 file: - access_level: open_access checksum: 35009d5fad01198341e6c1a3353481b7 content_type: application/pdf creator: system date_created: 2018-12-12T11:53:51Z date_updated: 2020-07-14T12:46:51Z file_id: '5512' file_name: IST-2014-305-v1+1_main.pdf file_size: 655774 relation: main_file file_date_updated: 2020-07-14T12:46:51Z has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: '12' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '305' related_material: record: - id: '1732' relation: later_version status: public - id: '5426' relation: later_version status: public status: public title: Qualitative analysis of POMDPs with temporal logic specifications for robotics applications type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '5426' abstract: - lang: eng text: We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty. 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: Martin full_name: Chmelik, Martin id: 3624234E-F248-11E8-B48F-1D18A9856A87 last_name: Chmelik - first_name: Raghav full_name: Gupta, Raghav last_name: Gupta - first_name: Ayush full_name: Kanodia, Ayush last_name: Kanodia citation: ama: Chatterjee K, Chmelik M, Gupta R, Kanodia A. Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications. IST Austria; 2014. doi:10.15479/AT:IST-2014-305-v2-1 apa: Chatterjee, K., Chmelik, M., Gupta, R., & Kanodia, A. (2014). Qualitative analysis of POMDPs with temporal logic specifications for robotics applications. IST Austria. https://doi.org/10.15479/AT:IST-2014-305-v2-1 chicago: Chatterjee, Krishnendu, Martin Chmelik, Raghav Gupta, and Ayush Kanodia. Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications. IST Austria, 2014. https://doi.org/10.15479/AT:IST-2014-305-v2-1. ieee: K. Chatterjee, M. Chmelik, R. Gupta, and A. Kanodia, Qualitative analysis of POMDPs with temporal logic specifications for robotics applications. IST Austria, 2014. ista: Chatterjee K, Chmelik M, Gupta R, Kanodia A. 2014. Qualitative analysis of POMDPs with temporal logic specifications for robotics applications, IST Austria, 10p. mla: Chatterjee, Krishnendu, et al. Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications. IST Austria, 2014, doi:10.15479/AT:IST-2014-305-v2-1. short: K. Chatterjee, M. Chmelik, R. Gupta, A. Kanodia, Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications, IST Austria, 2014. date_created: 2018-12-12T11:39:16Z date_published: 2014-09-29T00:00:00Z date_updated: 2023-02-23T12:25:47Z day: '29' ddc: - '005' department: - _id: KrCh doi: 10.15479/AT:IST-2014-305-v2-1 file: - access_level: open_access checksum: 730c0a8e97cf2712a884b2cc423f3919 content_type: application/pdf creator: system date_created: 2018-12-12T11:54:15Z date_updated: 2020-07-14T12:46:51Z file_id: '5537' file_name: IST-2014-305-v2+1_main2.pdf file_size: 656019 relation: main_file file_date_updated: 2020-07-14T12:46:51Z has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: '10' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '311' related_material: record: - id: '1732' relation: later_version status: public - id: '5424' relation: earlier_version status: public status: public title: Qualitative analysis of POMDPs with temporal logic specifications for robotics applications type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ...