On the complexity of equational decision problems for finite height complemented and orthocomplemented modular lattices

Abstract We study the computational complexity of satisfiability problem and complement equivalence for complemented (orthocomplemented) modular lattices L classes thereof. Concerning a simple finite height, $$\mathcal {NP}$$ NP -hardness is shown both problems. Moreover, problems are to be polynomial-time equivalent same feasibility over division ring D whenever subspace lattice -vector space dimension at least 3. Considering class all dimensional Hilbert spaces, ortholattices that endomorphism $$*$$ ∗ -rings with pseudo-inversion; moreover, we derive completeness Boolean part nondeterministic Blum-Shub-Smale model real computation without constants. This result extends additive category enriched by adjunction pseudo-inversion.