Complexity of the universal theory of bounded residuated distributive lattice-ordered groupoids
Dmitry Shkatov, C. J. Van Alten
TL;DR
This paper establishes that the universal and quasi-equational theories of bounded residuated distributive lattice-ordered groupoids are EXPTIME-complete, providing complexity classifications for these algebraic structures and related classes.
Contribution
It proves EXPTIME-completeness for the universal and quasi-equational theories of these algebraic structures, extending complexity results to related classes.
Findings
Universal and quasi-equational theories are EXPTIME-complete
Results apply to bounded distributive lattices with operators
Similar complexity results for specific classes of lattice-ordered groupoids
Abstract
We prove that the universal theory and the quasi-equational theory of bounded residuated distributive lattice-orderegroupoids are both EXPTIME-complete. Similar results areproven 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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