Formal Languages And Automata Theory Notes | Pdf

Convert NFA to DFA.

Prove aⁿbⁿcⁿ is not context-free using pumping lemma.

1. Introduction Formal Language: A set of strings (sequences of symbols) constrained by specific rules, formed over an alphabet (a finite set of symbols, denoted Σ). formal languages and automata theory notes pdf

Where: A, B are nonterminals; a is terminal; α, β, γ are strings of terminals/nonterminals.

An abstract self-operating machine (mathematical model) that processes strings and decides whether to accept or reject them. Convert NFA to DFA

Design CFG for balanced parentheses.

What are the capabilities and limitations of computing devices? 2. Basic Terminology | Term | Definition | Example | |------|------------|---------| | Alphabet (Σ) | Finite, non-empty set of symbols | Σ = a, b | | String (Word) | Finite sequence of symbols over Σ | aabb | | Empty String (ε) | String with zero symbols | ε | | Length | Number of symbols in a string | | aab | = 3 | | Kleene Star (Σ*) | Set of all possible strings over Σ (incl. ε) | ε, a, b, aa, ab, ... | | Kleene Plus (Σ⁺) | Σ* without ε | a, b, aa, ab, ... | | Language (L) | Any subset of Σ* | L = strings starting with 'a' | 3. Classification of Grammars (Chomsky Hierarchy) Noam Chomsky classified formal grammars into four types, each generating a specific class of languages. Introduction Formal Language: A set of strings (sequences

| Type | Grammar Name | Language Class | Automaton | Production Rule Form | |------|--------------|----------------|------------|----------------------| | Type 0 | Unrestricted | Recursively Enumerable | Turing Machine | α → β (any) | | Type 1 | Context-Sensitive | Context-Sensitive | Linear Bounded Automaton (LBA) | αAβ → αγβ (γ ≠ ε) | | Type 2 | Context-Free | Context-Free | Pushdown Automaton (PDA) | A → γ | | Type 3 | Regular | Regular | Finite Automaton (FA) | A → aB or A → a |