# Introduction to The Theory of Computation

Computation can be defined as the act of carrying out a computing calculation. In other words, computation is a type of calculation that includes both arithmetical and non-arithmetical steps that helps the computer solve problems through proper information processing.

The theory of computation can also be explained as a branch of computer science and mathematics that focuses on how effectively computer problems can be solved using the model of computation. It studies the general properties of computation which in turn helps to greatly increase the efficiency at which the computer solves problems.

In computer science, there are two major aspects that deal with solving the various problems that the computer encounters, these two aspects are the Theory of computation and the theory of programming. The theory of computation is more concerned with all checking the possibility and feasibility of solving a particular problem with the computer while the theory of programming involves the development of programs with methods that have been approved and regarded relevant by the theory of computation.

To fully understand the theory of computing, it has to be approached from three major fields. This field makes use of an algorithm to exploit the powers of the computer in solving problems, and they include:

1. Automata theory

2.Computability theory

3. Computational theory

A brief explanation of these three fields is given below.

## • Automata theory

The word automata originate from the Greek word autouta which means self-making. This theory was established in the 20th century, and its main aim is to analyse the behaviors of machines and how these machines solve problems. One of the most powerful models of this theory can be found in the Turing machine. This theory deals with the study of different types of abstract machines and the various computational problem they can be solved by these machines. The Turing machine is an example of these machines that are studied under this theory.

## • Computability theory

The computability theory was introduced in the 1930s by Kurt Godel, Alonzo Church, Alan Turing, Stephen Kleene, and Emil Post. These men helped to propose the compatibility theory that says that the development of real computers is based on theoretical models that involve solvable and unsolvable mathematical problems.

The computability knew as recursion theory is as a result of studded computable functions and Turing degrees.

## • Computational Complexity theory

The computational complexity theory discusses the efficiency at which the computer solves a particular problem. This efficiency analysed by comparing two major aspects of the problem-solving process, and these aspects include the time complexity and space complexity. These two aspects of the problem-solving process measure the number of steps needed to analyze and solve the problem thus determining the memory and space required to solve these problems.

When solving problems with the computer system, the problem under review or processing can either computationally hard or computationally easy. With these in mind, the next question that comes to mind is “what makes a problem computationally hard or computationally easy?” the answer to these questions is given below.

A problem is considered as “computationally hard” if it is easily solvable or can be efficiently solved by the computer. Examples of such problems are giving below.

### 2. Sorting out a sequence of numbers

Computationally hard problems, on the other hand, are problems that cannot be efficiently solved by the computer or that is impossible to determine if the problem will solve efficiently. Example of this type of “computationally hard” is given below

### 2. Computing a layout for chips in VSL

In most cases, problems relating to polynomial are regarded as computationally hard problems.

Now you may want to ask “why is computation so important?” or “ why is there so much emphasis placed on the computation theory?” Well, here are some reasons why the knowledge of the computation theory is so important to society.

When we encounter a lot of similar problems, we often try to solve these problems one after the other, and you will agree with me that it will more effective to develop a particular algorithm that can solve all these problems at once. But one major problem that developers face is creating a program that can solve all these problems at once, and this is almost impossible. To avoid wasting time trying to develop such a problem, it is more important to know which can be solved with algorithms and which problems cannot be solved with algorithms. Understanding this is one of the major functions of algorithms.

Another major importance of the computation theory is the understanding of how feasible the development of an algorithm is. In a case wherein the principle, the development of an algorithm is possible but is not feasible, the computation theory gives computer scientists the chance to know and also to make decisions on such an algorithm. Non-feasibility of an algorithm can be due to the extremely long time it might take for such an algorithm to be completed. This is another major importance of the computation theory in science and technology.

In summary, the theory of computation is important because it sets a theoretical foundation on what the computer can do and what it can not do.

In conclusion, since the computer is all about solving problems , the importance of the theory of computation can never be overemphasised. Computer scientists should have sound knowledge of computation so that they can effectively and efficiently take various problems with the computer system.

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