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.
@InProceedings{ganardi_et_al:LIPIcs.STACS.2017.35, author = {Ganardi, Moses and Hucke, Danny and K\"{o}nig, Daniel and Lohrey, Markus}, title = {{Circuit Evaluation for Finite Semirings}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {35:1--35:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.35}, URN = {urn:nbn:de:0030-drops-69978}, doi = {10.4230/LIPIcs.STACS.2017.35}, annote = {Keywords: circuit value problem, finite semirings, circuit complexity} }
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