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SEMIRINGS
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- Semirings are abundant because a suitable multiplication operation arises as the function composition of endomorphisms over any commutative monoid.
- Two typical semirings used in practice are the log semiring and tropical semiring: nondeterministic automata may be regarded as having weights in the Boolean semiring.
- Mathematical structures with an addition operation but not a subtraction operation include commutative semigroups, commutative monoids, and semirings.
- In mathematical analysis, idempotent analysis is the study of idempotent semirings, such as the tropical semiring.
- The semantics of Datalog have also been studied in the context of fixpoints over more general semirings.
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