Existential and universal width of alternating finite automata.
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| Title: | Existential and universal width of alternating finite automata. |
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| Authors: | Han, Yo-Sub1 (AUTHOR) emmous@yonsei.ac.kr, Kim, Sungmin1 (AUTHOR) rena_rio@yonsei.ac.kr, Ko, Sang-Ki1,2 (AUTHOR) sangkiko@uos.ac.kr, Salomaa, Kai1,3 (AUTHOR) salomaa@queensu.ca |
| Source: | Information & Computation. Sep2025, Vol. 306, pN.PAG-N.PAG. 1p. |
| Subjects: | Decidability (Mathematical logic), Computational complexity, Finite state machines |
| Abstract: | The existential width of an alternating finite automaton (AFA) A on a string w is, roughly speaking, the number of nondeterministic choices that A uses in an accepting computation on w that uses least nondeterminism. The universal width of A on string w is the least number of parallel branches an accepting computation of A on w needs to have. The existential or universal width of A is said to be finite if it is bounded for all accepted strings. We show that finiteness of existential and universal width of an AFA is decidable and at least PSPACE-hard. We consider the problem of deciding whether the existential or universal width is bounded by a given integer. We show that the problem is PSPACE-complete for AFAs where the number of transitions defined for a given universal state and input symbol is bounded by a constant. [ABSTRACT FROM AUTHOR] |
| Copyright of Information & Computation is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 187562701 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Existential and universal width of alternating finite automata. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Han%2C+Yo-Sub%22">Han, Yo-Sub</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> emmous@yonsei.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Kim%2C+Sungmin%22">Kim, Sungmin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rena_rio@yonsei.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Ko%2C+Sang-Ki%22">Ko, Sang-Ki</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> sangkiko@uos.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Salomaa%2C+Kai%22">Salomaa, Kai</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> salomaa@queensu.ca</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Information+%26+Computation%22">Information & Computation</searchLink>. Sep2025, Vol. 306, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Decidability+%28Mathematical+logic%29%22">Decidability (Mathematical logic)</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+state+machines%22">Finite state machines</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The existential width of an alternating finite automaton (AFA) A on a string w is, roughly speaking, the number of nondeterministic choices that A uses in an accepting computation on w that uses least nondeterminism. The universal width of A on string w is the least number of parallel branches an accepting computation of A on w needs to have. The existential or universal width of A is said to be finite if it is bounded for all accepted strings. We show that finiteness of existential and universal width of an AFA is decidable and at least PSPACE-hard. We consider the problem of deciding whether the existential or universal width is bounded by a given integer. We show that the problem is PSPACE-complete for AFAs where the number of transitions defined for a given universal state and input symbol is bounded by a constant. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Information & Computation is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.ic.2025.105337 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Decidability (Mathematical logic) Type: general – SubjectFull: Computational complexity Type: general – SubjectFull: Finite state machines Type: general Titles: – TitleFull: Existential and universal width of alternating finite automata. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Han, Yo-Sub – PersonEntity: Name: NameFull: Kim, Sungmin – PersonEntity: Name: NameFull: Ko, Sang-Ki – PersonEntity: Name: NameFull: Salomaa, Kai IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 08905401 Numbering: – Type: volume Value: 306 Titles: – TitleFull: Information & Computation Type: main |
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