Circuit Evaluation for Finite Semirings

Moses Ganardi; Danny Hucke; Daniel König; Markus Lohrey

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arXiv · 1602.04560

Circuit Evaluation for Finite Semirings

Moses Ganardi·Danny Hucke·Daniel König·Markus Lohrey

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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 $1 \neq 0$, then the circuit evaluation problem for the semiring is in $\mathsf{DET} \subseteq \mathsf{NC}^2$. In all other cases, the circuit evaluation problem is $\mathsf{P}$-complete.

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BibTeX RIS

Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey. 2016-02-15. Circuit Evaluation for Finite Semirings. https://arxiv.org/abs/1602.04560

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