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Bases for AC0 and Other Complexity Classes

Mazzanti S.

Fundamenta Informaticae

2015

Vol. 136, nr 4

433--460

Function complexity classes are defined as the substitution closure of finite function sets by improving a method of elimination of concatenation recursion from function algebras. Consequently, the set of AC0 functions and other canonical complexity classes are defined as the substitution closure of a finite function set.

CRN Elimination and Substitution Bases for Complexity Classes

Mazzanti S.

Fundamenta Informaticae

2012

Vol. 120, nr 1

29-58

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.