{"file_date_updated":"2022-05-17T07:51:08Z","abstract":[{"text":"Solving parity games, which are equivalent to modal μ-calculus model checking, is a central algorithmic problem in formal methods, with applications in reactive synthesis, program repair, verification of branching-time properties, etc. Besides the standard compu- tation model with the explicit representation of games, another important theoretical model of computation is that of set-based symbolic algorithms. Set-based symbolic algorithms use basic set operations and one-step predecessor operations on the implicit description of games, rather than the explicit representation. The significance of symbolic algorithms is that they provide scalable algorithms for large finite-state systems, as well as for infinite-state systems with finite quotient. Consider parity games on graphs with n vertices and parity conditions with d priorities. While there is a rich literature of explicit algorithms for parity games, the main results for set-based symbolic algorithms are as follows: (a) the basic algorithm that requires O(nd) symbolic operations and O(d) symbolic space; and (b) an improved algorithm that requires O(nd/3+1) symbolic operations and O(n) symbolic space. In this work, our contributions are as follows: (1) We present a black-box set-based symbolic algorithm based on the explicit progress measure algorithm. Two important consequences of our algorithm are as follows: (a) a set-based symbolic algorithm for parity games that requires quasi-polynomially many symbolic operations and O(n) symbolic space; and (b) any future improvement in progress measure based explicit algorithms immediately imply an efficiency improvement in our set-based symbolic algorithm for parity games. (2) We present a set-based symbolic algorithm that requires quasi-polynomially many symbolic operations and O(d · log n) symbolic space. Moreover, for the important special case of d ≤ log n, our algorithm requires only polynomially many symbolic operations and poly-logarithmic symbolic space.","lang":"eng"}],"volume":57,"date_created":"2022-03-18T12:46:32Z","publication_status":"published","publication":"22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning","language":[{"iso":"eng"}],"_id":"10883","scopus_import":"1","oa":1,"file":[{"content_type":"application/pdf","date_updated":"2022-05-17T07:51:08Z","success":1,"file_id":"11392","file_name":"2018_EPiCs_Chatterjee.pdf","creator":"dernst","access_level":"open_access","checksum":"1229aa8640bd6db610c85decf2265480","date_created":"2022-05-17T07:51:08Z","file_size":720893,"relation":"main_file"}],"day":"23","publisher":"EasyChair","department":[{"_id":"KrCh"}],"user_id":"72615eeb-f1f3-11ec-aa25-d4573ddc34fd","article_processing_charge":"No","oa_version":"Published Version","alternative_title":["EPiC Series in Computing"],"date_updated":"2022-07-29T09:24:31Z","status":"public","external_id":{"arxiv":["1909.04983"]},"author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","first_name":"Krishnendu","orcid":"0000-0002-4561-241X"},{"first_name":"Wolfgang","last_name":"Dvořák","full_name":"Dvořák, Wolfgang"},{"orcid":"0000-0002-5008-6530","first_name":"Monika H","last_name":"Henzinger","full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"full_name":"Svozil, Alexander","first_name":"Alexander","last_name":"Svozil"}],"conference":{"location":"Awassa, Ethiopia","start_date":"2018-11-17","name":"LPAR: Conference on Logic for Programming, Artificial Intelligence and Reasoning","end_date":"2018-11-21"},"ddc":["000"],"acknowledgement":"A. S. is fully supported by the Vienna Science and Technology Fund (WWTF) through project ICT15-003. K.C. is supported by the Austrian Science Fund (FWF) NFN Grant No S11407-N23 (RiSE/SHiNE) and an ERC Starting grant (279307: Graph Games). For M.H the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) /ERC Grant Agreement no. 340506.","page":"233-253","type":"conference","has_accepted_license":"1","doi":"10.29007/5z5k","intvolume":"        57","citation":{"chicago":"Chatterjee, Krishnendu, Wolfgang Dvořák, Monika H Henzinger, and Alexander Svozil. “Quasipolynomial Set-Based Symbolic Algorithms for Parity Games.” In <i>22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning</i>, 57:233–53. EasyChair, 2018. <a href=\"https://doi.org/10.29007/5z5k\">https://doi.org/10.29007/5z5k</a>.","apa":"Chatterjee, K., Dvořák, W., Henzinger, M. H., &#38; Svozil, A. (2018). Quasipolynomial set-based symbolic algorithms for parity games. In <i>22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning</i> (Vol. 57, pp. 233–253). Awassa, Ethiopia: EasyChair. <a href=\"https://doi.org/10.29007/5z5k\">https://doi.org/10.29007/5z5k</a>","ista":"Chatterjee K, Dvořák W, Henzinger MH, Svozil A. 2018. Quasipolynomial set-based symbolic algorithms for parity games. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning. LPAR: Conference on Logic for Programming, Artificial Intelligence and Reasoning, EPiC Series in Computing, vol. 57, 233–253.","mla":"Chatterjee, Krishnendu, et al. “Quasipolynomial Set-Based Symbolic Algorithms for Parity Games.” <i>22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning</i>, vol. 57, EasyChair, 2018, pp. 233–53, doi:<a href=\"https://doi.org/10.29007/5z5k\">10.29007/5z5k</a>.","short":"K. Chatterjee, W. Dvořák, M.H. Henzinger, A. Svozil, in:, 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, EasyChair, 2018, pp. 233–253.","ieee":"K. Chatterjee, W. Dvořák, M. H. Henzinger, and A. Svozil, “Quasipolynomial set-based symbolic algorithms for parity games,” in <i>22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning</i>, Awassa, Ethiopia, 2018, vol. 57, pp. 233–253.","ama":"Chatterjee K, Dvořák W, Henzinger MH, Svozil A. Quasipolynomial set-based symbolic algorithms for parity games. In: <i>22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning</i>. Vol 57. EasyChair; 2018:233-253. doi:<a href=\"https://doi.org/10.29007/5z5k\">10.29007/5z5k</a>"},"date_published":"2018-10-23T00:00:00Z","quality_controlled":"1","title":"Quasipolynomial set-based symbolic algorithms for parity games","project":[{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407","name":"Game Theory","call_identifier":"FWF"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307","call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications"}],"publication_identifier":{"issn":["2398-7340"]},"ec_funded":1,"month":"10","year":"2018"}