Computational Theory Questions Medium
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, and explores their properties and relationships. It also investigates the concept of computability, which refers to the ability to solve a problem using an algorithm or a computational procedure.
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 difficulty of algorithms by measuring the amount of time, space, or other resources they consume. Computational complexity theory aims to classify problems into different complexity classes based on their inherent difficulty and to understand the relationships between these classes. It introduces concepts such as time complexity, space complexity, and polynomial-time reductions to quantify and compare the efficiency of algorithms.
In summary, computational theory is a broader field that investigates the fundamental principles of computation, while computational complexity theory is a narrower subfield that focuses on analyzing the efficiency and difficulty of algorithms. Computational theory explores what can be computed, while computational complexity theory studies how efficiently it can be computed.