Wednesday, January 28

Proper Complexity Functions

Definition

Reason for needing such a definition (to avoid nonintuitive anomalies like the gap theorem).

Time Complexity Functions

What a time complexity class is.

Families of time complexity classes, like P and NP.

Complements of Languages

If SAT is the set of all strings that form a satisfiable boolean expression in conjunctive normal form, the the complement of SAT is the set of all strings that (1) do not form proper boolean expressions or (2) do form proper boolean expressions that are not satisfiable.  Most definitions of complement languages in the study of complexity theory ignore (1).  Papadimitriou at least makes some reference to this fact.  Just don't get confused yourself.