About Theory Of Computation : Automata theory (also known as Theory Of Computation) is a theoretical branch of Computer Science and Mathematics, which mainly deals with the logic of computation with respect to simple machines, referred to as automata.
Automata* enables the scientists to understand how machines compute the functions and solve problems. The main motivation behind developing Automata Theory was to develop methods to describe and analyse the dynamic behavior of discrete systems.
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More About Theory Of Computation :
In theoretical computer science and mathematics, the theory of computationis the branch of theoretical computer science that deals with how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: automata theory and languages,computability theory, and computational complexity theory, which are linked by the question: “What are the fundamental capabilities and limitations of computers?”.
In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several models in use, but the most commonly examined is theTuring machine. Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, and because it represents what many consider the most powerful possible “reasonable” model of computation (see Church–Turing thesis). It might seem that the potentially infinite memory capacity is an unrealizable attribute, but any decidable problem solved by a Turing machine will always require only a finite amount of memory. So in principle, any problem that can be solved (decided) by a Turing machine can be solved by a computer that has a finite amount of memory.
Areas of theory of computional:
1_Automata theory: Automata theory is the study of abstract computational devices. Abstract devices are (simplified) models of real computations.Computations happen everywhere: On your laptop, on your cell phone, in nature, …
2_Computability theory: Computability theory deals primarily with the question of the extent to which a problem is solvable on a computer. The statement that the halting problem cannot be solved by a Turing machine is one of the most important results in computability theory, as it is an example of a concrete problem that is both easy to formulate and impossible to solve using a Turing machine. Much of computability theory builds on the halting problem result.
3_Complexity theory: Complexity theory considers not only whether a problem can be solved at all on a computer, but also how efficiently the problem can be solved. Two major aspects are considered:
1. Time complexity: and how many steps does it take to perform a computation .
2. Space complexity:and how much memory is required to perform that computation.