The circuit equivalence problem Ceqv(A) of a finite algebra A is the problem of deciding whether two circuits over A compute the same function or not. This problem not only generalises the equivalence problem for Boolean circuits, but is also of interest in universal algebra, as it models the problem of checking identities in A. In this paper we prove that Ceqv(A) ∈ 𝖯, if A is a finite 2-nilpotent algebra from a congruence modular variety.
@InProceedings{kawalek_et_al:LIPIcs.STACS.2024.45, author = {Kawa{\l}ek, Piotr and Kompatscher, Michael and Krzaczkowski, Jacek}, title = {{Circuit Equivalence in 2-Nilpotent Algebras}}, booktitle = {41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)}, pages = {45:1--45:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-311-9}, ISSN = {1868-8969}, year = {2024}, volume = {289}, editor = {Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.45}, URN = {urn:nbn:de:0030-drops-197554}, doi = {10.4230/LIPIcs.STACS.2024.45}, annote = {Keywords: circuit equivalence, identity checking, nilpotent algebra} }
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