**Summary of the Theory of Computation and Its Dimensions**

Every programme in a computer is made of a different set of language and commands that helps in its smooth working. The field of computer science and mathematics uses the same to deal with the efficiency of solving computational models using the means of an algorithm. The theory of computation is a branch that highlights the study of such concepts. Let's delve deeper into the subject and know what are the different dimensions related to it.

**What is a theory of computation?**

It is defined as the creation of models in different areas of computer science. This branch uses the number theories i.e. mathematics and logic in the model of computation. It is further divided into three main branches that comprise of automata theory, computability theory and the third is the computational complexity theory. These theories help in explaining the fundamental capabilities of each of the source and thereby aids one in understanding the limitations to computations. Individuals can gain a complete insight into the subject by following the theory of computation pdf available across the internet platform. The main branches of theory of computation are-

- Automate Theory
- Computational complexity theory
- Computability Theory

**What is automata theory?**

The automata theory is elucidated as a branch of computational theory that aims in defining the designing of abstract computing devices which herein follows an already defined and predetermined sequence. The sequence of operation is determined automatically. This theory gains a high over the other concepts as its applicability is seen across numerous areas. An automaton plays an important role in the computational theory, artificial intelligence, formal verification, parsing and in compiler construction.

**What is the importance of automata theory?**

This theory happens to be the core of computer science as it includes study about computer hardware and software. The FA is an important model having its applicability in studying the automata computer hardware and software concepts. Moreover, it helps in elucidating two primary concepts of computation that is decidability and intractability, which undermines the questions about what can a computer do i.e. decide how to solve a problem, and what can a computer do efficiently i.e. solving problems using fewer functions.

**What are finite automata?**

There are numerous other theories that are included in this concept. These include finite automation and deterministic finite automaton. A finite automata is a finite number of states generated using a single automaton. In simpler words, it is defined as a simple idealized machine which is used for recognizing the patterns. These take their input from a few character sets or alphabets. The important aspect of an FA or finite automaton is either accepting or rejecting an input. This greatly depends on the aspect whether the pattern is defined by FA or not.

This is further divided into Nondeterministic Finite Automaton (NFA) and Deterministic Finite Automaton (DFA). An NFA means the transition can take place at multiple states at once. On the other hand, the Deterministic Finite Automaton or DFA is a process wherein it can be in and transition to only one state at a time.

It has to be understood that an NFA is not as powerful as a DFA as for constructing every NFA one needs to generate an equal number of DFA. However, both the formats use the same class of regular languages. In order to translate an NFA into a DFA, it is important to label each state in the DFA with the set of states in that of NFA.

**What are the advantages of finite automata?**

They are the most widely used form of automata as they are equivalent to regular expressions used in programming methods by developers in matching strings and for extracting texts. They help in describing various sets of strings with the use of basic characters, grouping and repetition method.

**What are pushdown automata?**

A **pushdown automata** is a form of FA that employs an extra memory stack. It helps in recognizing Context-free languages. They are less capable in front of Turning machines yet helps in understanding what can be computed using a machine. In case of this type of automata, the DFA is used to recognize the context-free languages whereas the Nondeterministic ones are used in reading all context-free languages along with those used in generating parser design.

**What is a formal language theory?**

The formal languages and automata theory are closely related to one another. Every automaton is defined as a finite representation of a formal language. This language can be an infinite set.

It is the predetermined basis for studying the theory of formal languages. These are divided into basic definitions comprising of a symbol, an alphabet, a word, and a language. It produces a set of strings using the formal language concept. Its applicability is seen across the areas of theoretical computer science, formal semantics, theoretical linguistics, logic in mathematics and much more.

**What is a number theory?**

Unlike the other theories mentioned above, a number theory which determines the basic algorithms used in the study of computer science and a part of TOC. This theory is particularly used for solving matrix type problems and puzzles using numbers instead of languages. Overall, all the concepts are interlinked to each other and gaining a proper idea about each is important for all those who deem to build their career in the said area.

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