On the Length of Shortest 2-Collapsing Words.
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| Title: | On the Length of Shortest 2-Collapsing Words. |
|---|---|
| Authors: | Cherubini, Alessandra1 alessandra.cherubini@polimi.it, Kisielewicz, Andrzej2 kisiel@math.uni.wroc.pl, Piochi, Brunetto3 piochi@math.unifi.it |
| Source: | Discrete Mathematics & Theoretical Computer Science (DMTCS). Jun2009, Vol. 11 Issue 1, p33-44. 12p. |
| Subjects: | Sequential machine theory, Vocabulary, Alphabet, Machine theory, Algorithms |
| Abstract: | Given a word w over a finite alphabet ∑ and a finite deterministic automaton A = (Q, ∑, δ), the inequality δ(Q, w))| ≤ |Q|- k means that under the natural action of the word w the image of the state set Q is reduced by at least k states. The word w is k-collapsing (k-synchronizing) if this inequality holds for any deterministic finite automaton (with k + 1 states) that satisfies such an inequality for at least one word. We prove that for each alphabet ∑ there is a 2-collapsing word whose length is |∑|³+6|∑|²+5|∑|/2 . Then we produce shorter 2-collapsing and 2-synchronizing words over alphabets of 4 and 5 letters. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete Mathematics & Theoretical Computer Science (DMTCS) is the property of Discrete Mathematics & Theoretical Computer Science DMTCS 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 | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 41021551 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: On the Length of Shortest 2-Collapsing Words. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Cherubini%2C+Alessandra%22">Cherubini, Alessandra</searchLink><relatesTo>1</relatesTo><i> alessandra.cherubini@polimi.it</i><br /><searchLink fieldCode="AR" term="%22Kisielewicz%2C+Andrzej%22">Kisielewicz, Andrzej</searchLink><relatesTo>2</relatesTo><i> kisiel@math.uni.wroc.pl</i><br /><searchLink fieldCode="AR" term="%22Piochi%2C+Brunetto%22">Piochi, Brunetto</searchLink><relatesTo>3</relatesTo><i> piochi@math.unifi.it</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Mathematics+%26+Theoretical+Computer+Science+%28DMTCS%29%22">Discrete Mathematics & Theoretical Computer Science (DMTCS)</searchLink>. Jun2009, Vol. 11 Issue 1, p33-44. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Sequential+machine+theory%22">Sequential machine theory</searchLink><br /><searchLink fieldCode="DE" term="%22Vocabulary%22">Vocabulary</searchLink><br /><searchLink fieldCode="DE" term="%22Alphabet%22">Alphabet</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+theory%22">Machine theory</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Given a word w over a finite alphabet ∑ and a finite deterministic automaton A = (Q, ∑, δ), the inequality δ(Q, w))| ≤ |Q|- k means that under the natural action of the word w the image of the state set Q is reduced by at least k states. The word w is k-collapsing (k-synchronizing) if this inequality holds for any deterministic finite automaton (with k + 1 states) that satisfies such an inequality for at least one word. We prove that for each alphabet ∑ there is a 2-collapsing word whose length is |∑|³+6|∑|²+5|∑|/2 . Then we produce shorter 2-collapsing and 2-synchronizing words over alphabets of 4 and 5 letters. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete Mathematics & Theoretical Computer Science (DMTCS) is the property of Discrete Mathematics & Theoretical Computer Science DMTCS 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 33 Subjects: – SubjectFull: Sequential machine theory Type: general – SubjectFull: Vocabulary Type: general – SubjectFull: Alphabet Type: general – SubjectFull: Machine theory Type: general – SubjectFull: Algorithms Type: general Titles: – TitleFull: On the Length of Shortest 2-Collapsing Words. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Cherubini, Alessandra – PersonEntity: Name: NameFull: Kisielewicz, Andrzej – PersonEntity: Name: NameFull: Piochi, Brunetto IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2009 Type: published Y: 2009 Identifiers: – Type: issn-print Value: 13658050 Numbering: – Type: volume Value: 11 – Type: issue Value: 1 Titles: – TitleFull: Discrete Mathematics & Theoretical Computer Science (DMTCS) Type: main |
| ResultId | 1 |
