上下文无关文法与语言的形式化描述

Formal languages and automata theory is a branch of theoretical computer science that studies formal languages, grammars, and automata. In the second lecture of this subject, the focus was on context-free grammars and context-free languages. Context-free grammars are a type of formal grammar that generate context-free languages. These grammars consist of a set of production rules that define how symbols can be replaced by other symbols. The language generated by a context-free grammar is called a context-free language, which can be recognized by a pushdown automaton. A context-free grammar is defined by a set of production rules of the form A -> α, where A is a non-terminal symbol and α is a string of terminal and non-terminal symbols. The starting symbol of the grammar is used to derive the entire language. Context-free languages have many applications in computer science, including parsing and compiling programming languages. They are used to define the syntax of programming languages and to generate parsers that can recognize valid programs written in those languages. Overall, the study of context-free grammars and context-free languages is an important topic in formal languages and automata theory. It provides a theoretical foundation for understanding the structure and properties of formal languages and automata, as well as their practical applications in computer science.