Complexity Class - Relationships Between Complexity Classes

Relationships Between Complexity Classes

The following table shows some of the classes of problems (or languages, or grammars) that are considered in complexity theory. If class X is a strict subset of Y, then X is shown below Y, with a dark line connecting them. If X is a subset, but it is unknown whether they are equal sets, then the line is lighter and is dotted. Technically, the breakdown into decidable and undecidable pertains more to the study of computability theory but is useful for putting the complexity classes in perspective.

Decision Problem
Type 0 (Recursively enumerable)
Undecidable
Decidable
EXPSPACE
NEXPTIME
EXPTIME
PSPACE
Type 1 (Context Sensitive)
Co-NP
BQP
NP
BPP
P
NC
Type 2 (Context Free)
Type 3 (Regular)

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