Cristopher Moore, Denis Thérien, François Lemieux, Joshua Berman, Arthur Drisko  Home/Search
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Abstract: We consider circuits and expressions whose gates carry out multiplication in a non-associative groupoid such as a quasigroup or loop. We define a class we call the polyabelian groupoids, formed by iterated quasidirect products of Abelian groups. We show that a quasigroup can express arbitrary Boolean functions if and only if it is not polyabelian, in which case its Expression Evaluation and Circuit Value problems are NC¹-complete and P-complete respectively. This is not true or groupoids... (Update)
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...computational complexity. Evaluating circuits and expressions in such a groupoid are P complete and NC 1 complete respectively [15], and solving equations of constants and variables in non solvable groups is NP complete [9] On the other hand, if a groupoid lacks this...
...no such theory exists for context free languages. Nevertheless, this topic has been the subjet of recent investigations (e.g. [18, 21, 10, 13, 19, 7, 8, 20]) that we briefly describe here. A groupoid G is a set with a binary operation that can be non associative. All groupoids...
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BibTeX entry: (Update)
F. Lemieux, C. Moore, D. Therien, J. Berman, and A. Drisko, \Circuits and Expressions with Non-Associative Gates." To appear in J. Comput. System Sci. http://citeseer.ist.psu.edu/395248.html More
@article{ moore00circuits,
author = "Cristopher Moore and Denis Therien and Francois Lemieux and Joshua Berman and Arthur Drisko",
title = "Circuits and Expressions with Nonassociative Gates",
journal = "Journal of Computer and System Sciences",
volume = "60",
number = "2",
pages = "368-394",
year = "2000",
url = "citeseer.ist.psu.edu/395248.html" }
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