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Formal Language And Its Type.finite automata and formal languages

Formal Language And Its Type.finite automata and formal languages

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๐Ÿ“˜ Formal Language and Its Types | Finite Automata and Formal Languages

Formal language and automata theory form the mathematical foundation of computer science, especially compiler design, language processing, and artificial intelligence.


๐Ÿ” What is a Formal Language?

A formal language is a set of strings made from a finite alphabet and governed by specific syntactic rules. It is used to define and analyze languages that computers can process.


Types of Formal Languages (Chomsky Hierarchy)

Language Class Automaton / Recognizer Grammar Type Example Language
1โƒฃ Regular Languages Finite Automata (FA) Type 3 โ€“ Regular Binary numbers divisible by 3
2โƒฃ Context-Free Languages Pushdown Automata (PDA) Type 2 โ€“ CFG Balanced parentheses ((()))
3โƒฃ Context-Sensitive Linear Bounded Automata (LBA) Type 1 โ€“ CSG a^n b^n c^n where n โ‰ฅ 1
4โƒฃ Recursively Enumerable Turing Machine (TM) Type 0 โ€“ Unrestricted All computable languages

Finite Automata (FA)

Used to recognize regular languages. There are two main types:

1. DFA (Deterministic Finite Automaton)

2. NFA (Non-Deterministic Finite Automaton)

Formal Definition of DFA:

DFA = (Q, ฮฃ, ฮด, q0, F)
Q  = set of states
ฮฃ  = input alphabet
ฮด  = transition function (Q ร— ฮฃ โ†’ Q)
q0 = initial state
F  = set of accepting states

Applications of Formal Languages


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