Computational Theory Questions Long
Computational theory and computational complexity theory are two distinct branches of computer science that focus on different aspects of computation.
Computational theory, also known as the theory of computation, is concerned with understanding the fundamental principles and capabilities of computation. It aims to answer questions such as what can be computed, how efficiently it can be computed, and what are the limits of computation. Computational theory encompasses various models of computation, including Turing machines, finite automata, and lambda calculus, among others. It explores the theoretical foundations of computation and investigates the properties and limitations of different computational models.
On the other hand, computational complexity theory is a subfield of computational theory that specifically deals with the study of the resources required to solve computational problems. It focuses on analyzing the efficiency and complexity of algorithms and problems, aiming to classify problems based on their inherent difficulty and the resources needed to solve them. Computational complexity theory introduces measures such as time complexity, space complexity, and other resources like communication complexity or circuit complexity to quantify the resources required by algorithms. It also introduces complexity classes, such as P, NP, and NP-complete, to classify problems based on their computational difficulty.
In summary, computational theory is a broader field that investigates the fundamental principles of computation, while computational complexity theory is a subfield within computational theory that focuses on analyzing the efficiency and complexity of algorithms and problems. Computational theory explores what can be computed, while computational complexity theory studies how efficiently it can be computed.