Preservation theorems hold for all lattice semirings but fail for tropical, Viterbi, Łukasiewicz, and natural semirings, while existential preservation holds on finite interpretations for lattices unlike the Boolean case.
Homomorphism preservation theorems
2 Pith papers cite this work. Polarity classification is still indexing.
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For forbidden families of odd cycles and cliques, the edge-coloring problem with forbidden patterns is poly-time equivalent to its precolored version and to a finite CSP, yielding a P versus NP-complete dichotomy.
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Preservation Theorems in Semiring Semantics
Preservation theorems hold for all lattice semirings but fail for tropical, Viterbi, Łukasiewicz, and natural semirings, while existential preservation holds on finite interpretations for lattices unlike the Boolean case.
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Edge-coloring problems with forbidden patterns and planted colors
For forbidden families of odd cycles and cliques, the edge-coloring problem with forbidden patterns is poly-time equivalent to its precolored version and to a finite CSP, yielding a P versus NP-complete dichotomy.