Finite Automata

Last Updated on March 16, 2023 by Prepbytes

An Finite Automata’s job is to accept or reject an input based on whether the pattern defined by the Finite Automata appears in the input. Finite automata have two states: Accept and Reject. It will accept when the input string is successfully processed and the automata have reached their final state. In this section, we will discuss Finite Automata, types of finite automata, and Applications of finite automata.

What are Finite Automata?

Finite automata are simple abstract machines used to recognize patterns. Finite automata are also known as a finite-state machines. It is a mathematical model of a system with discrete inputs, output, states, and a set of transitions from state to state that occurs on input alphabets symbols. In simple words, we can say It has a set of states and rules for moving from one state to the next, but it is dependent on the input symbol used.

The diagram above depicts the following characteristics of automata:

• Input
• Output
• States of automata
• State relation
• Output relation

Finite automata is a collection of 5 tuples (Q, ∑, δ, q0, F), in which

Q: Finite set of states.
Σ: set of Input Symbols.
q: Initial state.
F: set of Final States.
δ: Transition Function.

Types of Finite Automata

There are two types of finite automata

1. DFA
2. NFA

1. DFA

It refers to Deterministic Finite Automation, which has a fixed number of states and each input symbol uniquely determines the next state. In simple words, it accepts input if the last state is final. Backtracking can be possible in DFA. It requires more space.DFA is a subset of NFA.DFA is hard to construct

DFA is a five-tuple automata:

M=(Q, Σ, δ,q0,F)

Where

Q: Finite set called states.
Σ: Finite set called alphabets.
δ: Q × Σ → Q is the transition function.
q0 ϵ Q is the start or initial state.
F: Final or accept state.

2. NFA

It refers to Non-Determinstic Automata. It is finite automata in which there exist many paths for specific input from the current state to the next state. NFA is easy to construct as compared to DFA. Backtracking is not always possible, requires less space, and permits empty string transition .it also has five states.

δ: Q X Σ → 2Q

Where

Q: Finite set of states
Σ: Finite set of the input symbol
q0: Initial state
F: Final state
δ: Transition function

Application of Finite Automata

• Finite automata have various applications in computer science which include lexical analysis, parsing, and pattern matching, and also used to create compilers
• Finite automata used in Networking Protocols to detect errors and ensure that the data transfer between the devices is reliable or not
• Finite automata used in the digital circuit. They can be used to design, logic gates.
• Finite automata is highly useful to design spell checkers

Conclusion
Now we can conclude that finite automata are computational models which used to recognize patterns and generate regular language .mainly there are two types of finite automata DFA and NFA. DFA requires more space and it is hard to implement if compare with NFA. Finite automata used to create compilers are also used in digital circuits and have various applications in computer science which include lexical analysis, parsing, and pattern matching

Frequently Asked Questions(FAQs)

Here are some FAQs on finite automata:

Q1: What is the difference between a complete and an incomplete finite automaton?
A: A complete finite automaton has a transition defined for every possible input symbol from every state, while an incomplete finite automaton may have some missing transitions. Incomplete automata are sometimes used for simplicity, but they may require additional checks to ensure that all input strings are properly handled.

Q2: What is the difference between an accepting state and a rejecting state in a finite automaton?
A: An accepting state is a state in a finite automaton where the automaton accepts the input string and halts, while a rejecting state is a state where the automaton does not accept the input string and halts.

Q3: What is the minimization of a finite automaton?
A: The minimization of a finite automaton is the process of finding an equivalent automaton with the smallest number of states possible. This can be useful in simplifying the automaton and making it easier to analyze.

Q4: What is the difference between a language and a grammar?
A: A language is a set of strings that can be generated by a particular formal system, while a grammar is a set of rules that describe how to generate the strings in that language. Finite automata can be used to recognize regular languages, while context-free grammars and pushdown automata are used to recognize context-free languages.

Q5: Can finite automata recognize non-regular languages?
A: No, finite automata can only recognize regular languages. There are many languages that are not regular, and these cannot be recognized by any finite automaton.

Q6: What is the complement of a language?
A: The complement of a language is the set of all strings that are not in the language. For example, if a language contains all strings that start with the letter ‘a’, then its complement contains all strings that do not start with ‘a’.

Q7: What is the difference between a prefix, suffix, and substring of a string?
A: A prefix of a string is a substring that appears at the beginning of the string. A suffix of a string is a substring that appears at the end of the string. A substring of a string can be any contiguous set of characters within the string.