Complexity Column

Descriptive complexity theory initiated by celebrated Fagin's theorem aims to characterize complexity classes by the kind of logic necessary to express problems in the class. For many complexity classes such a characterization has been found; this includes the class NP that, according to Fagin's theorem, can be characterized by the monadic second order logic. Some classes, however, eludes such a characterization, and this famously includes the class P. Due to the importance of the class P, finding a logic for P is one of the central open problems in descriptive complexity.