Predicate classes and promise classes

Abstract

Considering computation trees produced by polynomial time nondeterministic computations one can define a complexity class by any predicate on computation trees, such classes will be called predicate classes. It will be shown that these classes are exactly the principal ideals of the polynomial time many-one reducibility. Additionally, the set of classes-which are called promise classes-definable by promise functions instead of predicates are shown to be equal to the set of countable ideals.<>