New substitution bases for complexity classes

The set 0(), the 0 closure of F , is the closure with respect to substitution and concatenation recursion on notation of a set of basic functions comprehending the set F . By improving earlier work, we show that 0() is the substitution closure of a simple function set and characterize well\u2010known function complexity classes as the substitution closure of finite sets of simple functions

CRN elimination and Substitution Bases for Complexity Classes

Function classes closed with respect to substitution and concatenation recursion on notation are characterized as the substitution closure of finite function sets. Consequently, the sets of TC0, NC1 and L computable functions are characterized as the substitution closure of a finite function set