We study the computational complexity of checking identities in a fixed finite monoid. We prove that this problem is coNP-complete for the monoid of all full transformations of a 4-element set. This result completes the description of the complexity of checking identities in the transformation monoids.
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Lanzhou Univ, Dept Math & Stat, Lanzhou 730000, Gansu, Peoples R China
Key Lab Appl Math & Complex Syst, Lanzhou, Gansu, Peoples R ChinaUniv Vienna, Fak Math, A-1090 Vienna, Austria
Chen, Yuzhu
Hu, Xun
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Lanzhou Univ, Dept Math & Stat, Lanzhou 730000, Gansu, Peoples R China
Key Lab Appl Math & Complex Syst, Lanzhou, Gansu, Peoples R China
Chongqing Technol & Business Univ, Dept Math & Stat, Chongqing 400033, Peoples R ChinaUniv Vienna, Fak Math, A-1090 Vienna, Austria
Hu, Xun
Luo, Yanfeng
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Lanzhou Univ, Dept Math & Stat, Lanzhou 730000, Gansu, Peoples R China
Key Lab Appl Math & Complex Syst, Lanzhou, Gansu, Peoples R ChinaUniv Vienna, Fak Math, A-1090 Vienna, Austria
Luo, Yanfeng
Volkov, M. V.
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Ural Fed Univ, Inst Math & Comp Sci, Ekaterinburg 620000, RussiaUniv Vienna, Fak Math, A-1090 Vienna, Austria