Abstract
Presented here are an algebra and a logic characterizing the complexity class NC 1 , which consists of functions computed by uniform families of polynomial size, log depth circuits. In both characterizations, NC 1 functions are regarded as functions from one class of finite relational structures to another. In the algebraic characterization a recursion scheme called upward tree recursion is applied to a class of simple functions. In the logical characterization, first-order logic is augmented by an operator for defining relations by primitive recursion where it is assumed that every structure has an underlying relation BIT giving the binary representations of integers.
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.
