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Complexity of the universal theory of bounded residuated distributive lattice-ordered groupoids

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Abstract

We prove that the universal theory and the quasi-equational theory of bounded residuated distributive lattice-ordered groupoids are both EXPTIME-complete. Similar results are proven for bounded distributive lattices with a unary or binary operator and for some special classes of bounded residuated distributive lattice-ordered groupoids.

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Acknowledgements

We are indebted to the anonymous reviewers for their suggestions that have helped to improve the paper.

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  1. School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa

    Dmitry Shkatov & C. J. Van Alten

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  1. Dmitry Shkatov
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  2. C. J. Van Alten
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Correspondence to C. J. Van Alten.

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Dmitry Shkatov acknowledges support from the Russian Foundation for Basic Research, projects 17-03-00818 and 18-011-00869.

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Shkatov, D., Van Alten, C.J. Complexity of the universal theory of bounded residuated distributive lattice-ordered groupoids. Algebra Univers. 80, 36 (2019). https://doi.org/10.1007/s00012-019-0609-1

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