The Theory of Computation is a branch of computer science and mathematics that focuses on determining problems that can be solved mechanically, using an algorithm or a set of programming rules. It is also concerned with the efficiency at which the algorithm can perform the solution.
In simple terms, the Theory of Computation answers these questions:
- What problems can the machine solve? What problems can’t it solve?
- How fast can a machine solve a problem?
- How much memory space does a machine need to solve a problem?
To answer these questions, computer scientists use a model of computation, which is a computer simulation for the algorithm being developed. The Turing machine is among the most used models of computation.
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The Theory of Computation rests on the fact that computers can’t solve all problems. A given machine would have limitations, and the Theory of Computation aims to discover these. The computational model is given inputs and decides whether or not it can process the information using the developed algorithm.
For example, you can create a machine and design it so that it only accepts red objects. The algorithm is pretty straightforward, as represented by the image below. The red square is accepted, and the model rejects the yellow square.
The Theory of Computation can also help determine if a model needs improvement. In the example above, the developer may want to introduce other inputs to see how the model treats them. What happens when a red square with a yellow border is introduced to the machine? How about when the border is red, but the inside of the object is yellow?
Three Main Branches of the Theory of Computation
Three theories make up what the Theory of Computation is. These are:
- Automata Theory: Refers to the analysis of how machines work to solve a problem.
- Computability Theory: Pertains to determining which problems a machine can solve and which ones it can’t.
- Computational Complexity Theory: Addresses the issue of the efficiency of the machine when solving a problem.
One of the most famous inventions that embody these concepts is the Turing machine created by Alan Turing in the 1930s. The idea is that a Turing machine can run any problem that algorithms can solve. In reverse, anything that an algorithm can’t do can’t be done by a Turing machine.
The video below shows a simple implementation of the Turing machine.
What Is the Theory of Computation For?
In the real world, the theory has helped with several projects. For one, a group of computer scientists used the theory to test a book vending machine design. Register machine models are also based on the Theory of Computation, among other things.
The theory is applicable to other fields besides computer science, such as engineering and life and social sciences. It is also a fundamental concept in artificial intelligence (AI), natural language processing (NLP), neural networks, and the like.
The Theory of Computation is a basic concept that computer scientists should understand. After all, it reflects the reality of life—no single solution can solve all problems. As such, it is often included in the computer science curriculum of universities.
Given a set of problems, it would be a waste of time and effort for computer scientists to create one algorithm to solve all of them. The Theory of Computation dictates that developers first determine which problems can be solved algorithmically and which ones can’t. After that, they would also need to find out how efficient the algorithm would be in terms of time and memory space spent solving the problem.