Computational complexity theory

INTRODUCTION Computational complexity is the study of the resources, such as time and space (memory), required to solve computational problems. By quantifying these resources, complexity theory has profoundly affected our thinking about computation. Computability theory establishes the existence of undecidable problems that cannot be solved in principle, regardless of the amount of time invested. In contrast, complexity theory establishes the existence of decidable problems that, although solvable in principle, cannot be solved in practice, because the time and space required would be larger than the age and size of the known universe [Stockmeyer and Chandra 1979]. The quest for the boundaries of the set of feasible problems, those solvable in practice, has led to one of the most important unresolved questions in computer science: Is P different from NP? Here P comprises the problems that can be solved feasibly in polynomial tim