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Linear equations with min and max operators: Computational complexity

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Τίτλος: Linear equations with min and max operators: Computational complexity
Συγγραφείς: Chatterjee, Krishnendu, Luo, Ruichen, Saona Urmeneta, Raimundo J, Svoboda, Jakub
Πηγή: Chatterjee K, Luo R, Saona Urmeneta RJ, Svoboda J. Linear equations with min and max operators: Computational complexity. In: Proceedings of the 39th AAAI Conference on Artificial Intelligence . Vol 39. Association for the Advancement of Artificial Intelligence; 2025:11150-11157. doi: 10.1609/aaai.v39i11.33212
Στοιχεία εκδότη: Association for the Advancement of Artificial Intelligence
Έτος έκδοσης: 2025
Συλλογή: IST Austria Research Explorer (Institute of Science and Technology)
Περιγραφή: We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability condition; (C2) the non-negative coefficients condition; (C3) the sum upto 1 condition; and (C4) the only min or only max operator condition. Several seminal results in the literature focus on special cases. For example, turn-based stochastic games correspond to conditions C2 and C3; and Markov decision process to conditions C2, C3, and C4. However, the systematic computational complexity study of all the cases has not been explored, which we address in this work. Some highlights of our results are: with conditions C2 and C4, and with conditions C3 and C4, the problem is NP-complete, whereas with condition C1 only, the problem is in UP intersects coUP. Finally, we establish the computational complexity of the decision problem of checking the respective conditions.
Τύπος εγγράφου: conference object
report
Γλώσσα: English
ISSN: 2159-5399
2374-3468
Relation: info:eu-repo/semantics/altIdentifier/issn/2159-5399; info:eu-repo/semantics/altIdentifier/e-issn/2374-3468; info:eu-repo/semantics/altIdentifier/arxiv/2412.12228
Διαθεσιμότητα: https://research-explorer.ista.ac.at/record/19669
Rights: info:eu-repo/semantics/openAccess
Αριθμός Καταχώρησης: edsbas.79E608FE
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  Data: Linear equations with min and max operators: Computational complexity
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  Data: Chatterjee K, Luo R, Saona Urmeneta RJ, Svoboda J. Linear equations with min and max operators: Computational complexity. In: Proceedings of the 39th AAAI Conference on Artificial Intelligence . Vol 39. Association for the Advancement of Artificial Intelligence; 2025:11150-11157. doi: 10.1609/aaai.v39i11.33212
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  Data: We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability condition; (C2) the non-negative coefficients condition; (C3) the sum upto 1 condition; and (C4) the only min or only max operator condition. Several seminal results in the literature focus on special cases. For example, turn-based stochastic games correspond to conditions C2 and C3; and Markov decision process to conditions C2, C3, and C4. However, the systematic computational complexity study of all the cases has not been explored, which we address in this work. Some highlights of our results are: with conditions C2 and C4, and with conditions C3 and C4, the problem is NP-complete, whereas with condition C1 only, the problem is in UP intersects coUP. Finally, we establish the computational complexity of the decision problem of checking the respective conditions.
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