Where: A, B are nonterminals; a is terminal; α, β, γ are strings of terminals/nonterminals.
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
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. Where: A, B are nonterminals; a is terminal;
Design CFG for balanced parentheses.