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In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer.
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. [1] Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements.
NC = P problem The P vs NP problem is a major unsolved question in computer science that asks whether every problem whose solution can be quickly verified by a computer (NP) can also be quickly solved by a computer (P). This question has profound implications for fields such as cryptography, algorithm design, and computational theory.
The study of the relationships between complexity classes is a major area of research in theoretical computer science. There are often general hierarchies of complexity classes; for example, it is known that a number of fundamental time and space complexity classes relate to each other in the following way: L ⊆ NL ⊆ P ⊆ NP ⊆ PSPACE ⊆ ...
Computational complexity theory deals with how hard computations are, in quantitative terms, both with upper bounds (algorithms whose complexity in the worst cases, as use of computing resources, can be estimated), and from below (proofs that no procedure to carry out some task can be very fast).
The theory of computation can be considered the creation of models of all kinds in the field of computer science. Therefore, mathematics and logic are used. In the last century, it separated from mathematics and became an independent academic discipline with its own conferences such as FOCS in 1960 and STOC in 1969, and its own awards such as the IMU Abacus Medal (established in 1981 as the ...
A finite-state automaton from automata theory, a branch of theoretical computer science. Theoretical computer science is a subfield of computer science and mathematics that focuses on the abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely.
Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, () below stands in for the complexity of the chosen multiplication algorithm.