Fast Symbolic Algorithms for Omega-Regular Games under Strong Transition Fairness
We consider fixpoint algorithms for two-player games on graphs with $\omega$-regular winning conditions, where the environment is constrained by a strong transition fairness assumption. Strong transition fairness is a widely occurring special case of strong fairness, which requires that any executio...
Gespeichert in:
| Veröffentlicht in: | TheoretiCS Jg. 2 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
TheoretiCS Foundation e.V
24.02.2023
|
| Schlagworte: | |
| ISSN: | 2751-4838, 2751-4838 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | We consider fixpoint algorithms for two-player games on graphs with
$\omega$-regular winning conditions, where the environment is constrained by a
strong transition fairness assumption. Strong transition fairness is a widely
occurring special case of strong fairness, which requires that any execution is
strongly fair with respect to a specified set of live edges: whenever the
source vertex of a live edge is visited infinitely often along a play, the edge
itself is traversed infinitely often along the play as well. We show that,
surprisingly, strong transition fairness retains the algorithmic
characteristics of the fixpoint algorithms for $\omega$-regular games -- the
new algorithms have the same alternation depth as the classical algorithms but
invoke a new type of predecessor operator. For Rabin games with $k$ pairs, the
complexity of the new algorithm is $O(n^{k+2}k!)$ symbolic steps, which is
independent of the number of live edges in the strong transition fairness
assumption. Further, we show that GR(1) specifications with strong transition
fairness assumptions can be solved with a 3-nested fixpoint algorithm, same as
the usual algorithm. In contrast, strong fairness necessarily requires
increasing the alternation depth depending on the number of fairness
assumptions. We get symbolic algorithms for (generalized) Rabin, parity and
GR(1) objectives under strong transition fairness assumptions as well as a
direct symbolic algorithm for qualitative winning in stochastic
$\omega$-regular games that runs in $O(n^{k+2}k!)$ symbolic steps, improving
the state of the art. Finally, we have implemented a BDD-based synthesis engine
based on our algorithm. We show on a set of synthetic and real benchmarks that
our algorithm is scalable, parallelizable, and outperforms previous algorithms
by orders of magnitude. |
|---|---|
| AbstractList | We consider fixpoint algorithms for two-player games on graphs with
$\omega$-regular winning conditions, where the environment is constrained by a
strong transition fairness assumption. Strong transition fairness is a widely
occurring special case of strong fairness, which requires that any execution is
strongly fair with respect to a specified set of live edges: whenever the
source vertex of a live edge is visited infinitely often along a play, the edge
itself is traversed infinitely often along the play as well. We show that,
surprisingly, strong transition fairness retains the algorithmic
characteristics of the fixpoint algorithms for $\omega$-regular games -- the
new algorithms have the same alternation depth as the classical algorithms but
invoke a new type of predecessor operator. For Rabin games with $k$ pairs, the
complexity of the new algorithm is $O(n^{k+2}k!)$ symbolic steps, which is
independent of the number of live edges in the strong transition fairness
assumption. Further, we show that GR(1) specifications with strong transition
fairness assumptions can be solved with a 3-nested fixpoint algorithm, same as
the usual algorithm. In contrast, strong fairness necessarily requires
increasing the alternation depth depending on the number of fairness
assumptions. We get symbolic algorithms for (generalized) Rabin, parity and
GR(1) objectives under strong transition fairness assumptions as well as a
direct symbolic algorithm for qualitative winning in stochastic
$\omega$-regular games that runs in $O(n^{k+2}k!)$ symbolic steps, improving
the state of the art. Finally, we have implemented a BDD-based synthesis engine
based on our algorithm. We show on a set of synthetic and real benchmarks that
our algorithm is scalable, parallelizable, and outperforms previous algorithms
by orders of magnitude. We consider fixpoint algorithms for two-player games on graphs with $\omega$-regular winning conditions, where the environment is constrained by a strong transition fairness assumption. Strong transition fairness is a widely occurring special case of strong fairness, which requires that any execution is strongly fair with respect to a specified set of live edges: whenever the source vertex of a live edge is visited infinitely often along a play, the edge itself is traversed infinitely often along the play as well. We show that, surprisingly, strong transition fairness retains the algorithmic characteristics of the fixpoint algorithms for $\omega$-regular games -- the new algorithms have the same alternation depth as the classical algorithms but invoke a new type of predecessor operator. For Rabin games with $k$ pairs, the complexity of the new algorithm is $O(n^{k+2}k!)$ symbolic steps, which is independent of the number of live edges in the strong transition fairness assumption. Further, we show that GR(1) specifications with strong transition fairness assumptions can be solved with a 3-nested fixpoint algorithm, same as the usual algorithm. In contrast, strong fairness necessarily requires increasing the alternation depth depending on the number of fairness assumptions. We get symbolic algorithms for (generalized) Rabin, parity and GR(1) objectives under strong transition fairness assumptions as well as a direct symbolic algorithm for qualitative winning in stochastic $\omega$-regular games that runs in $O(n^{k+2}k!)$ symbolic steps, improving the state of the art. Finally, we have implemented a BDD-based synthesis engine based on our algorithm. We show on a set of synthetic and real benchmarks that our algorithm is scalable, parallelizable, and outperforms previous algorithms by orders of magnitude. |
| Author | Banerjee, Tamajit Majumdar, Rupak Schmuck, Anne-Kathrin Soudjani, Sadegh Mallik, Kaushik |
| Author_xml | – sequence: 1 givenname: Tamajit surname: Banerjee fullname: Banerjee, Tamajit – sequence: 2 givenname: Rupak surname: Majumdar fullname: Majumdar, Rupak – sequence: 3 givenname: Kaushik surname: Mallik fullname: Mallik, Kaushik – sequence: 4 givenname: Anne-Kathrin surname: Schmuck fullname: Schmuck, Anne-Kathrin – sequence: 5 givenname: Sadegh surname: Soudjani fullname: Soudjani, Sadegh |
| BookMark | eNp1kM9LwzAUgINMcM7dPeYf6EzSpE2PY7g5GAzdPIfXJO0y2kaS7rD_3v0QFcHTezze9x2-ezTofGcReqRkwjNWyKd-Z32wvdNxwtIJv0FDlguacJnKwa_9Do1j3BNCWMEET8UQvc4h9nhzbEvfOI2nTe2D63dtxJUPeN3aGpI3Wx8aCHgBrY340Bkb8KYPvqvxNkAXXe98h-fgQmdjfEC3FTTRjr_mCL3Pn7ezl2S1Xixn01WiaZHxhFkqaVFKU1JegUyBGgsk0xpyxjMLTIIudFkQbqSl1uhUVlTkJKe5MSQr0xFaXr3Gw159BNdCOCoPTl0OPtQKwqlIY9XpW9ACSJkSySsuCsikNKCF0IYC5ycXubp08DEGW337KFGXwuqnsGKpOiPZH0S7Hs4l-gCu-R_8BHTFh3M |
| CitedBy_id | crossref_primary_10_1016_j_nahs_2023_101430 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION DOA |
| DOI | 10.46298/theoretics.23.4 |
| DatabaseName | CrossRef DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| EISSN | 2751-4838 |
| ExternalDocumentID | oai_doaj_org_article_6b3519a0b3084f459a688dac55cd1a44 10_46298_theoretics_23_4 |
| GroupedDBID | AAFWJ AAYXX ADQAK AFPKN ALMA_UNASSIGNED_HOLDINGS CITATION GROUPED_DOAJ M~E |
| ID | FETCH-LOGICAL-c1964-2e1819b8db14fa83a1dea06cca7246ea28ac9cb904d8e1edc38f1570717dd06b3 |
| IEDL.DBID | DOA |
| ISSN | 2751-4838 |
| IngestDate | Tue Oct 14 19:03:13 EDT 2025 Sat Nov 29 01:37:36 EST 2025 Tue Nov 18 22:43:26 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| License | https://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c1964-2e1819b8db14fa83a1dea06cca7246ea28ac9cb904d8e1edc38f1570717dd06b3 |
| OpenAccessLink | https://doaj.org/article/6b3519a0b3084f459a688dac55cd1a44 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_6b3519a0b3084f459a688dac55cd1a44 crossref_primary_10_46298_theoretics_23_4 crossref_citationtrail_10_46298_theoretics_23_4 |
| PublicationCentury | 2000 |
| PublicationDate | 2023-02-24 |
| PublicationDateYYYYMMDD | 2023-02-24 |
| PublicationDate_xml | – month: 02 year: 2023 text: 2023-02-24 day: 24 |
| PublicationDecade | 2020 |
| PublicationTitle | TheoretiCS |
| PublicationYear | 2023 |
| Publisher | TheoretiCS Foundation e.V |
| Publisher_xml | – name: TheoretiCS Foundation e.V |
| SSID | ssj0002925435 |
| Score | 2.211195 |
| Snippet | We consider fixpoint algorithms for two-player games on graphs with
$\omega$-regular winning conditions, where the environment is constrained by a
strong... We consider fixpoint algorithms for two-player games on graphs with $\omega$-regular winning conditions, where the environment is constrained by a strong... |
| SourceID | doaj crossref |
| SourceType | Open Website Enrichment Source Index Database |
| SubjectTerms | computer science - formal languages and automata theory computer science - symbolic computation electrical engineering and systems science - systems and control |
| Title | Fast Symbolic Algorithms for Omega-Regular Games under Strong Transition Fairness |
| URI | https://doaj.org/article/6b3519a0b3084f459a688dac55cd1a44 |
| Volume | 2 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2751-4838 dateEnd: 20241231 omitProxy: false ssIdentifier: ssj0002925435 issn: 2751-4838 databaseCode: DOA dateStart: 20220101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2751-4838 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002925435 issn: 2751-4838 databaseCode: M~E dateStart: 20220101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELZQxcCCQIAoL3lgYQh1HDu2x4IILJS3xBb5lVKJtigtSCz8dnxOKWWBhSVDdI6i7yzfXXL3fQgdhqRTCCdIQnkFBYqSidFhL4fYLqzmuVepiWIToteTj4_qekHqC3rCGnrgBrhObkBCThOTEckqxpXOpXTacm5dqllkAiVCLRRTcAZTBUPevPkvyXKqZGc-GDg5ptkx-xGHFuj6Y1wp1tDqLCHE3eZF1tGSH22gm0JPpvjufWiAthd3n_vjUMQ_DSc45Jj4auj7OrmNKvI1Poc-VwyzYDW-gw_bfRwDUOzFwoUe1HCabaKH4uz-9CKZiR8kFjiyEupD7FVGOpOySstMp85rkgfABWW511Rqq6xRhDnpU-9sJquUCyjPnCMBtS3UGo1HfhvhYOik5LmkxgO_nyaZ5yRXTmTMVD5ro84XFKWdMYODQMVzGSqECF75DV5Js5K10dF8xUvDivGL7QmgO7cDPut4I3i5nHm5_MvLO__xkF20AmLxcSCd7aHWtH71-2jZvk0Hk_ogbqBwvfw4-wQ_s878 |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Fast+Symbolic+Algorithms+for+Omega-Regular+Games+under+Strong+Transition+Fairness&rft.jtitle=TheoretiCS&rft.au=Banerjee%2C+Tamajit&rft.au=Majumdar%2C+Rupak&rft.au=Mallik%2C+Kaushik&rft.au=Schmuck%2C+Anne-Kathrin&rft.date=2023-02-24&rft.issn=2751-4838&rft.eissn=2751-4838&rft.volume=2&rft_id=info:doi/10.46298%2Ftheoretics.23.4&rft.externalDBID=n%2Fa&rft.externalDocID=10_46298_theoretics_23_4 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2751-4838&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2751-4838&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2751-4838&client=summon |