Introduction to the Theory of Computation (TOC)

In the year 1930, the mathematicians & logicians have started the research on computation to know the meaning. At present, the TOC (Theory of Computation) can be separated into three theories like computability theory, complexity theory, as well as automata theory. The TOC is a scientific control troubled with the study of computation properties like natural, artificial, and otherwise imaginary. Most considerably, it plans to know the environment of resourceful computation. The TOC in computer science & mathematics is the division that deals with computation to solve the problems using an algorithm. To know about this concept, there is the different theory of computation books available in the market namely “an introduction to automata theory languages and computation”. This article gives an overview of the theory of computation notes.

What is the Theory of Computation?

The theory of computation is also known as Automata theory. This is a theoretical division of mathematics as well as computer science, which mostly deals with the computation logic with respect to automata. Automata theory allows the researchers to know how machines calculate the functions as well as resolve problems.


The main intention of developing this theory was to extend techniques to explain and examine the active performance of discrete systems. The name of automata is invented from the name automaton. Because it is similar to the term Automation”.The automata theory or theory of computation mainly deals with computation forms & revises their descriptions & properties. The best examples of this theory mainly include finite automata, Turing machines & contest free grammars.

Basic Terminologies of TOC

Now, let’s know the necessary terminologies of TOC which are significant as well as often used.


It is the least building block like some alphabet, picture or any letter.



These are a set of symbols and can be denoted with Σ. Alphabets are for all time fixed. The best examples of alphabets include the following.

Σ = {0,1}

It is the binary digit’s alphabet.

Σ = {0,1,……,9}

It is the decimal digit’s alphabet.

Σ = {a,b,c}

Σ = {A, B,C,….Z}


  • It is a limited series of symbols from several alphabets, and generally, it is denoted with as well as string’s length can be denoted with |w|.
  • An empty string with zero amounts of symbols can be denoted with ‘ε’.
  • No.of strings can be generated over the {a, b} alphabets like a, ab, ba, and bb.
  • From the above information string’s length is |w| = 2, and a number of strings are 4.
  • For {a, b} alphabets with ‘n’ length, the no.of strings can be produced is 2n.


It is a set of strings, selected from Σ*, and it can also be defined as, it is a division of Σ* ‘, and it can be created over ‘ Σ ‘ which can be limited or endless.

For example: For finite language L1= [ set of the entire strings of length 2}

{aa, ab, ba, bb}

For infinite language L2= [ set of the entire strings which begins with ‘a’}

{a, aa, ab, aba,aaa, abb}

Influences of ‘ Σ ‘

When Σ = {a,b} subsequently

Σ0 = Set of the entire strings above Σ with 0 lengths {ε}

Σ1 = Set of the entire strings above Σ with 1 length{a, b}

Σ2 = Set of the entire strings above Σ with 2 length {aa, ab, ba, bb}

That is, |Σ2|= 4 & also, |Σ3| = 8

Σ*-Universal Set.

Σ* = Σ0 * U Σ1 * U Σ2

= {ε}*U {a, b}* U {aa, ab, ba, bb}( infinite language.)


Cardinality is the no. of the elements within the set.

Transition Function

An automaton is invented to work in a separate time edge at a single point of time, and the control unit is in some internal state & the input device will scan a certain symbol on the input tape. The internal state of this control unit at the next point of time or step is called the next state or the transition function.

This transition function gives the next state in terms of the current state, the current input symbol on the input tape, and the information currently in the temporary storage. During the transition from the one step to the next step, the output may get generated or the information in the temporary storage may get changed.


The word configuration mainly refers to an exact control unit state, the temporary storage & the i/p tape. A move can be defined as it is the conversion from one phase to the next phase.

Theory of Computation Benefits

The TOC concept will teach you regarding the basic ways in which a PC can be ready to imagine. There is an immense agreement of work that was made feasible in the part of NLP (Natural Language Processing) that involved in constructing of FSMs (Finite State Machines) which is also known as FSA (Finite State Automata).

Know the mathematical rules leading proficient computation, & apply this realizing to address troubles happening in other computer science & mathematics parts, and also in extra fields like physics as well as neuroscience.

Research Areas of TOC

The research areas of theory of computation mainly involve in the following areas.

  • Cryptography
  • Design & Analysis of Algorithms
  • Quantum Calculation
  • Logic within Computer Science
  • Computational Difficulty
  • Randomness within Calculation
  • Correcting Errors in Codes

Thus, this is all about the theory of computation tutorial. It is the basic course of computer science, and will assist you to know how people have thought about this like computer science is a science in the past few years. It is mostly about what type of equipment you can actually calculate automatically and how quick you can perform it as well as how much gap does it obtain to do so. This is the study of theoretical computational devices. Calculations occur all over like on your PC, cell phone, and also in nature. Here is a question for you, what are good theory of computation books, please leave in the comment.