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Circuit Evaluation for Finite Semirings

Authors Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey

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Moses Ganardi
Danny Hucke
Daniel König
Markus Lohrey

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Moses Ganardi, Danny Hucke, Daniel König, and Markus Lohrey. Circuit Evaluation for Finite Semirings. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.STACS.2017.35

Abstract

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 R (i) has a solvable multiplicative semigroup and (ii) does not contain a subsemiring with an additive identity 0 and a multiplicative identity 1 != 0, then its circuit evaluation problem is in the complexity class DET (which is contained in NC^2). In all other cases, the circuit evaluation problem is P-complete.

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Keywords
  • circuit value problem
  • finite semirings
  • circuit complexity

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