Lecture 13 Introduction to Computational Complexity: Problem Classification

Concept of asymptotic scaling of resources for digitised problems is introduced, together with logical relations between problems. Hierarchy of computational complexity classes for decision problems is defined: P, NP, PP, PSPACE. NP-complete and BPP problems are defined. Quantum extensions to BQP and QMA are pointed out. Dependence of complexity on phrasing of the problem is emphasised. General Boolean logic problem is shown to be a linear algebra problem.