Automata on Infinite Trees with Equality and Disequality Constraints Between Siblings
This article is inspired by two works from the early 90s. The first one is by Bogaert and Tison who considered a model of automata on finite ranked trees where one can check equality and disequality constraints between direct subtrees: they proved that this class of automata is closed under Boolean...
Saved in:
| Published in: | Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science pp. 227 - 236 |
|---|---|
| Main Authors: | , , |
| Format: | Conference Proceeding |
| Language: | English |
| Published: |
New York, NY, USA
ACM
05.07.2016
|
| Series: | ACM Conferences |
| Subjects: | |
| ISBN: | 9781450343916, 1450343910 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | This article is inspired by two works from the early 90s. The first one is by Bogaert and Tison who considered a model of automata on finite ranked trees where one can check equality and disequality constraints between direct subtrees: they proved that this class of automata is closed under Boolean operations and that both the emptiness and the finiteness problem of the accepted language are decidable. The second one is by Niwinski who showed that one can compute the cardinality of any ω-regular language of infinite trees.
Here, we generalise the model of automata of Tison and Bogaert to the setting of infinite binary trees. Roughly speaking we consider parity tree automata where some transitions are guarded and can be used only when the two direct sub-trees of the current node are equal/disequal. We show that the resulting class of languages encompasses the one of ω-regular languages of infinite trees while sharing most of its closure properties, in particular it is a Boolean algebra. Our main technical contribution is then to prove that it also enjoys a decidable cardinality problem. In particular, this implies the decidability of the emptiness problem. |
|---|---|
| AbstractList | This article is inspired by two works from the early 90s. The first one is by Bogaert and Tison who considered a model of automata on finite ranked trees where one can check equality and disequality constraints between direct subtrees: they proved that this class of automata is closed under Boolean operations and that both the emptiness and the finiteness problem of the accepted language are decidable. The second one is by Niwinski who showed that one can compute the cardinality of any ω-regular language of infinite trees.
Here, we generalise the model of automata of Tison and Bogaert to the setting of infinite binary trees. Roughly speaking we consider parity tree automata where some transitions are guarded and can be used only when the two direct sub-trees of the current node are equal/disequal. We show that the resulting class of languages encompasses the one of ω-regular languages of infinite trees while sharing most of its closure properties, in particular it is a Boolean algebra. Our main technical contribution is then to prove that it also enjoys a decidable cardinality problem. In particular, this implies the decidability of the emptiness problem. |
| Author | Löding, Christof Carayol, Arnaud Serre, Olivier |
| Author_xml | – sequence: 1 givenname: Arnaud surname: Carayol fullname: Carayol, Arnaud email: Arnaud.Carayol@univ-mlv.fr organization: LIGM (Univ. Paris Est & CNRS) – sequence: 2 givenname: Christof surname: Löding fullname: Löding, Christof email: loeding@informatik.rwth-aachen.de organization: RWTH Aachen University, Germany – sequence: 3 givenname: Olivier surname: Serre fullname: Serre, Olivier email: Olivier.Serre@cnrs.fr organization: IRIF (Univ. Paris Diderot & CNRS) |
| BookMark | eNqNkDFPwzAYRC0BElAys3pkSfBnx3E8llCgUiUG2tlybAcMqSNiVxX_niDCznQ63dMN7xKdhiE4hK6BFAAlv6WSMS54MWXJSXmCMinqaSCsZBKqc5TF-E4IoSBqSeAC7ZaHNOx10ngIeB06H3xyeDs6F_HRpze8-jzo3qcvrIPF9z66v94MIaZR-5AivnPp6FzAL77tfXiNV-is03102ZwLtHtYbZunfPP8uG6Wm1wzQlMupGPEgoOOc1N3lJWWsEpULTXcSg5asMraWkgrjKlAg6RctLrSFmpjgbIFuvn91Wav2mH4iAqI-jGhZhNqNjGhxT9R1Y7edewbhVxhJw |
| ContentType | Conference Proceeding |
| Copyright | 2016 ACM |
| Copyright_xml | – notice: 2016 ACM |
| DOI | 10.1145/2933575.2934504 |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EndPage | 236 |
| GroupedDBID | 6IE 6IF 6IG 6IL 6IN AAJGR ACM ADPZR ALMA_UNASSIGNED_HOLDINGS APO BEFXN BFFAM BGNUA BKEBE BPEOZ CBEJK GUFHI IEGSK IJVOP OCL RIB RIC RIE RIL RIO |
| ID | FETCH-LOGICAL-a302t-79e30d1e1f55c8f234d03676b2c5d951a736dd879d7cc61a19257ba6ad18cd123 |
| ISBN | 9781450343916 1450343910 |
| ISICitedReferencesCount | 4 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000387609200023&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| IngestDate | Wed Jan 31 06:44:04 EST 2024 Wed Jan 31 06:45:21 EST 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | true |
| Keywords | Automata on infinite trees Automata with equality and disequality constraints Emptiness problem Finiteness problem |
| Language | English |
| License | Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions@acm.org |
| LinkModel | OpenURL |
| MeetingName | LICS '16: 31st Annual ACM/IEEE Symposium on Logic in Computer Science |
| MergedId | FETCHMERGED-LOGICAL-a302t-79e30d1e1f55c8f234d03676b2c5d951a736dd879d7cc61a19257ba6ad18cd123 |
| OpenAccessLink | https://hal.science/hal-01804545 |
| PageCount | 10 |
| ParticipantIDs | acm_books_10_1145_2933575_2934504 acm_books_10_1145_2933575_2934504_brief |
| PublicationCentury | 2000 |
| PublicationDate | 20160705 |
| PublicationDateYYYYMMDD | 2016-07-05 |
| PublicationDate_xml | – month: 07 year: 2016 text: 20160705 day: 05 |
| PublicationDecade | 2010 |
| PublicationPlace | New York, NY, USA |
| PublicationPlace_xml | – name: New York, NY, USA |
| PublicationSeriesTitle | ACM Conferences |
| PublicationTitle | Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science |
| PublicationYear | 2016 |
| Publisher | ACM |
| Publisher_xml | – name: ACM |
| SSID | ssj0002178901 |
| Score | 1.9844655 |
| Snippet | This article is inspired by two works from the early 90s. The first one is by Bogaert and Tison who considered a model of automata on finite ranked trees where... |
| SourceID | acm |
| SourceType | Publisher |
| StartPage | 227 |
| SubjectTerms | Theory of computation Theory of computation -- Formal languages and automata theory Theory of computation -- Logic |
| Title | Automata on Infinite Trees with Equality and Disequality Constraints Between Siblings |
| WOSCitedRecordID | wos000387609200023&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1ba9swFBZp2cOedutYuwsaDPYQvPku6THNOjZYukLT0TdjSzIYEmfYTmlhP37nWJLjdoNtD3uxk4MjE33H1nckne8Q8obLEEsihV4aJxCgCK08wUXhKc3Arv1S9jUjv31hp6f88lKcTSY_XC7M1YrVNb--Ft__K9RgA7AxdfYf4B4aBQN8BtDhCLDD8Q4j_u3gczYYW7f-HwVtN7VC-rP5AprGEG96frPGLVvbNS4YYM1laVIATZkH99SPfWq27TbAcHP8wee6rJCvTpeN1jZH7sSkaBpJpw8VbtM237EsaF-Momunx3Zn2HlVrMbT9PO8yW9Mva8ZuPdWDXuFcDH_OFW2-oqVQyiHuSHdmHn0r6sKB3nznkT95hYcbTHKabw1xRGk_XbYZOSUi1tRbxAnftRnDI_fvEZiwA7ioVFV-XV8iFFKAyhOBDT1HZyhqXiP7DHmm9y_YX4OQjUOXKnPBbS3GyTC3O2tVBQY3t9pErmOXI-YyvIhOdj9X7rzhUdkouvH5IFDl1p0n5ALByrd1NSBSntQKYJKHagUQKUjUOkIVGpBpQ7UA3Lx8WQ5_-TZWhteHvlh5zGhI18FOiiTRPIyjGLlo5hfEcpEAQvPWZQqxZlQTMo0yCEwSFiRp7kKuFRAf56S_XpT62eElhCFAnMH7s6iWJRaQASLCqERT3NZiOCQvIa-yfCRaTOTF59ktv8y23-H5O0fr8kK8KTy6C9ae07u79zqBdnvmq1-Se7Jq65qm1c97j8BANRuPw |
| linkProvider | IEEE |
| 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%3Abook&rft.genre=proceeding&rft.title=Proceedings+of+the+31st+Annual+ACM%2FIEEE+Symposium+on+Logic+in+Computer+Science&rft.atitle=Automata+on+Infinite+Trees+with+Equality+and+Disequality+Constraints+Between+Siblings&rft.au=Carayol%2C+Arnaud&rft.au=L%C3%B6ding%2C+Christof&rft.au=Serre%2C+Olivier&rft.series=ACM+Conferences&rft.date=2016-07-05&rft.pub=ACM&rft.isbn=9781450343916&rft.spage=227&rft.epage=236&rft_id=info:doi/10.1145%2F2933575.2934504 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=9781450343916/lc.gif&client=summon&freeimage=true |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=9781450343916/mc.gif&client=summon&freeimage=true |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=9781450343916/sc.gif&client=summon&freeimage=true |