"In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other."
It encompasses the study of the computational complexity of problems and the resources, such as time and space, required by different algorithms to solve them.
"A computational problem is a task solved by a computer."
"A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used."
"The theory formalizes this intuition by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage."
"Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity), and the number of processors (used in parallel computing)."
"One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do."
"The P versus NP problem, one of the seven Millennium Prize Problems, is dedicated to the field of computational complexity."
"Closely related fields in theoretical computer science are analysis of algorithms and computability theory."
"A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem."
"Computational complexity theory tries to classify problems that can or cannot be solved with appropriately restricted resources."
"Imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kinds of problems can, in principle, be solved algorithmically."
"Theory formalizes this intuition by introducing mathematical models of computation to study these problems and quantifying their computational complexity."
"A computational problem is a task solved by a computer."
"Mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage."
"A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used."
"Imposing restrictions on the available resources is what distinguishes computational complexity from computability theory."
"Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity), and the number of processors (used in parallel computing)."
"One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do."
"The P versus NP problem, one of the seven Millennium Prize Problems, is dedicated to the field of computational complexity."
"Imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kinds of problems can, in principle, be solved algorithmically."