The analysis and research on computational complexity

Computational complexity is a branch of the theory of computation. It is used to measure how hard a problem is solved and the common measures include time and space. The classes of time complexity generally include: P, NP, NP-hard, NP-complete and EXPTIME; the classes of space complexity generally include: PSPACE, NPSPACE, PSPACE-hard and PSPACE-complete. Researching computational complexity of a problem can make it explicit whether there is an effective solving algorithm of the problem or not. This paper introduces and analyzes some fundamental concepts of computational complexity, and discusses complete problems of time complexity and space complexity by examples; What´s more, the relation among complexity classes is analyzed in detail.