Abstract
We consider the complexity of various computational problems over nonassociative algebraic structures. Specifically, we look at the problem of evaluating circuits, formulas, and words, over both nonassociative structures themselves and over matrices with elements in these structures. Extending past work, we show that such problems can characterize a wide variety of complexity classes up to and including NP. As an example, the word (i.e., iterated multiplication) problems involving a sequence of O(logkn) matrices over a structure ( S; +, ·) in which (S; +) is a monoid or an aperiodic monoid are complete for NCk+1 and for ACk, respectively, and a word problem variant involving matrices of size O(logkn) is complete for SCk.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
