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Semiring is an algebraic system⟨ S,+,·⟩ such that⟨ S,+⟩ is a commutative semigroup,⟨ S,·⟩ is a semigroup, the multiplication is distributive over the addition. If there is an element 0 in the semiring S, such that x+ 0= 0+ x= x and x· 0= 0· x= 0 for all x∈ S, then we call S a semiring with a zero 0.