A tractability gap beyond nim-sums: It's hard to tell whether a bunch of superstars are losers.
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| Title: | A tractability gap beyond nim-sums: It's hard to tell whether a bunch of superstars are losers. |
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| Authors: | Burke, Kyle1 (AUTHOR) kburke@flsouthern.edu, Ferland, Matthew2 (AUTHOR) ferlandm@dickinson.edu, Huntemann, Svenja1,3 (AUTHOR) svenja.huntemann@msvu.ca, Teng, Shang-Hua4 (AUTHOR) shanghua@usc.edu |
| Source: | Theoretical Computer Science. Feb2026, Vol. 1062, pN.PAG-N.PAG. 1p. |
| Subjects: | Game theory, Computational complexity, Games |
| Abstract: | In this paper, we address a natural question at the intersection of combinatorial game theory and computational complexity: "Can a sum of simple tepid games in canonical form be intractable?" To resolve this fundamental question, we consider superstars , positions first introduced in Winning Ways where all options are nimbers. Extending Morris' classic result with hot games to tepid games, we prove that disjunctive sums of superstars are intractable to solve. This is striking as sums of nimbers can be computed in linear time. Our analysis shows that the game Paint Can is intractable and also yields a new intractable game, Blackout. We present web-playable versions of both games. [ABSTRACT FROM AUTHOR] |
| Copyright of Theoretical Computer Science is the property of Elsevier B.V. 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: 190262920 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A tractability gap beyond nim-sums: It's hard to tell whether a bunch of superstars are losers. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Burke%2C+Kyle%22">Burke, Kyle</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kburke@flsouthern.edu</i><br /><searchLink fieldCode="AR" term="%22Ferland%2C+Matthew%22">Ferland, Matthew</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> ferlandm@dickinson.edu</i><br /><searchLink fieldCode="AR" term="%22Huntemann%2C+Svenja%22">Huntemann, Svenja</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> svenja.huntemann@msvu.ca</i><br /><searchLink fieldCode="AR" term="%22Teng%2C+Shang-Hua%22">Teng, Shang-Hua</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> shanghua@usc.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Theoretical+Computer+Science%22">Theoretical Computer Science</searchLink>. Feb2026, Vol. 1062, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Game+theory%22">Game theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Games%22">Games</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we address a natural question at the intersection of combinatorial game theory and computational complexity: "Can a sum of simple tepid games in canonical form be intractable?" To resolve this fundamental question, we consider superstars , positions first introduced in Winning Ways where all options are nimbers. Extending Morris' classic result with hot games to tepid games, we prove that disjunctive sums of superstars are intractable to solve. This is striking as sums of nimbers can be computed in linear time. Our analysis shows that the game Paint Can is intractable and also yields a new intractable game, Blackout. We present web-playable versions of both games. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Theoretical Computer Science is the property of Elsevier B.V. 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=190262920 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.tcs.2025.115656 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Game theory Type: general – SubjectFull: Computational complexity Type: general – SubjectFull: Games Type: general Titles: – TitleFull: A tractability gap beyond nim-sums: It's hard to tell whether a bunch of superstars are losers. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Burke, Kyle – PersonEntity: Name: NameFull: Ferland, Matthew – PersonEntity: Name: NameFull: Huntemann, Svenja – PersonEntity: Name: NameFull: Teng, Shang-Hua IsPartOfRelationships: – BibEntity: Dates: – D: 02 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 03043975 Numbering: – Type: volume Value: 1062 Titles: – TitleFull: Theoretical Computer Science Type: main |
| ResultId | 1 |
