Subsemiring

The following dichotomy is shown: If a finite semiring is such that (i) the multiplicative semigroup is solvable and (ii) it does not contain a subsemiring with an additive identity 0 and a multiplicative identity 1#92;neq 0, then the circuit evaluation problem for the semiring is in #92;mathsf#123;DET#125;#92;subseteq#92;mathsf#123;NC#125;².