Abstract: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 0 and a multiplicative identity 1 = 0, then the circuit evaluation problem for the semiring is in DET ⊆ NC 2 . In all other cases, the circuit evaluation … Show more
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