Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Context-Free Grammars: Part 2

Description

This lecture covers context-free grammars, including the definition of non-terminal and terminal symbols, rules for generating strings, and the concept of derivations. It also explores the use of automata and stack operations in the context of grammars.

Official source

Related concepts (13)

Context-free grammar

In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form with a single nonterminal symbol, and a string of terminals and/or nonterminals ( can be empty). Regardless of which symbols surround it, the single nonterminal on the left hand side can always be replaced by on the right hand side.

Context-free language

In formal language theory, a context-free language (CFL) is a language generated by a context-free grammar (CFG). Context-free languages have many applications in programming languages, in particular, most arithmetic expressions are generated by context-free grammars. Different context-free grammars can generate the same context-free language. Intrinsic properties of the language can be distinguished from extrinsic properties of a particular grammar by comparing multiple grammars that describe the language.

Context-sensitive grammar

A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that there are languages that can be described by a CSG but not by a context-free grammar. Context-sensitive grammars are less general (in the same sense) than unrestricted grammars.

Ambiguous grammar

In computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation or parse tree. Every non-empty context-free language admits an ambiguous grammar by introducing e.g. a duplicate rule. A language that only admits ambiguous grammars is called an inherently ambiguous language. Deterministic context-free grammars are always unambiguous, and are an important subclass of unambiguous grammars; there are non-deterministic unambiguous grammars, however.

Deterministic context-free grammar

In formal grammar theory, the deterministic context-free grammars (DCFGs) are a proper subset of the context-free grammars. They are the subset of context-free grammars that can be derived from deterministic pushdown automata, and they generate the deterministic context-free languages. DCFGs are always unambiguous, and are an important subclass of unambiguous CFGs; there are non-deterministic unambiguous CFGs, however. DCFGs are of great practical interest, as they can be parsed in linear time and in fact a parser can be automatically generated from the grammar by a parser generator.

Related lectures (32)

Context-Free Grammars

Covers context-free grammars, their equivalence to pushdown automata, and the hierarchy of grammar types.

Context-Free Grammars: Part 1

Covers context-free grammars, production rules, automata, syntax analysis, and parsing techniques.

CYK Algorithm for Parsing General Grammars

Explores parsing general grammars using the CYK algorithm and Chomsky Normal Form.

Introduction to Grammars

Introduces automata, regular languages limitations, context-free grammars, and balanced parentheses grammars.

CYK Parsing Algorithm for General Grammars