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Circuit Evaluation for Finite Semirings
The computational complexity of the circuit evaluation problem for finite
semirings is considered, where semirings are not assumed to have an additive or
multiplicative identity. 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 and a multiplicative
identity , then the circuit evaluation problem for the semiring is in
. In all other cases, the circuit
evaluation problem is -complete.Comment: Some proof details from the previous version are simplified in the
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