Podcast
Questions and Answers
The problem of determining whether a string is in the language generated by a context-free grammar arises in many applications, such as in the construction of ______.
The problem of determining whether a string is in the language generated by a context-free grammar arises in many applications, such as in the construction of ______.
compilers
One way to approach this problem is to begin with S and attempt to derive cbab using a series of ______.
One way to approach this problem is to begin with S and attempt to derive cbab using a series of ______.
productions
The approach that we have used is called ______ parsing, because it begins with the starting symbol and proceeds by successively applying productions.
The approach that we have used is called ______ parsing, because it begins with the starting symbol and proceeds by successively applying productions.
top-down
There is another approach to this problem, called ______ parsing. In this approach, we work backward.
There is another approach to this problem, called ______ parsing. In this approach, we work backward.
Using the production S → AB shows that a complete derivation for cbab is ______.
Using the production S → AB shows that a complete derivation for cbab is ______.
Which production rule is used to derive the string cbab from the non-terminal C?
Which production rule is used to derive the string cbab from the non-terminal C?
What is the first step in the top-down parsing approach for deriving cbab?
What is the first step in the top-down parsing approach for deriving cbab?
Which production is used to replace B during the derivation of the string cbab?
Which production is used to replace B during the derivation of the string cbab?
In bottom-up parsing, what is the final production rule applied to derive the string cbab from the starting symbol?
In bottom-up parsing, what is the final production rule applied to derive the string cbab from the starting symbol?
Which approach to parsing starts with the string and works backward?
Which approach to parsing starts with the string and works backward?
Flashcards are hidden until you start studying
Study Notes
Types of Phrase-Structure Grammars
- Phrase-structure grammars are classified based on allowed production types.
- Type 0 Grammar: No restrictions on productions.
- Type 1 Grammar: Productions are in the form w1 → w2, where w1 = lAr, w2 = lwr, with nonterminal symbols and nonempty strings.S → λ is permitted, except when S is on the right-hand side of other productions.
- Type 2 Grammar: Productions limited to w1 → w2, where w1 is a single non-terminal symbol. Also known as context-free grammars which generate context-free languages.
- Type 3 Grammar: Productions of the form w1 → w2, with w1 as a nonterminal and w2 either aB or a, known as regular grammars. Regular grammars produce regular languages.
Context-Free and Regular Grammars
- Context-free grammars define the syntax of nearly all programming languages; they effectively generate a variety of languages.
- Efficient algorithms allow verification of string generation via context-free grammars.
- Regular grammars are essential in pattern searching and lexical analysis, transforming input streams to token streams for parsers.
Examples of Languages
- The language {0*^n^1^n^* | n = 0, 1, 2,...} is context-free due to productions S → 0S1 and S → λ, but not regular.
- The set {0n1n2n | n = 0, 1, 2,...} is context-sensitive, generated by a type 1 grammar, but cannot be produced by type 2 grammars.
Derivation Trees
- A derivation tree, or parse tree, graphically represents derivations in context-free languages.
- The root symbolizes the starting symbol; internal nodes are nonterminal symbols, and leaves are terminal symbols.
- Each production A → w maps the vertex representing A to children vertices that represent each symbol in w.
Parsing Approaches
- Top-Down Parsing: Begins with the start symbol, applying productions to derive a string, exemplified by deriving cbab starting from S.
- Bottom-Up Parsing: Works backward from the target string, using productions to reconstruct the derivation, demonstrating how cbab can be formed from productions to reach the starting symbol S.
Types of Phrase-Structure Grammars
- Phrase-structure grammars are classified based on allowed production types.
- Type 0 Grammar: No restrictions on productions.
- Type 1 Grammar: Productions are in the form w1 → w2, where w1 = lAr, w2 = lwr, with nonterminal symbols and nonempty strings.S → λ is permitted, except when S is on the right-hand side of other productions.
- Type 2 Grammar: Productions limited to w1 → w2, where w1 is a single non-terminal symbol. Also known as context-free grammars which generate context-free languages.
- Type 3 Grammar: Productions of the form w1 → w2, with w1 as a nonterminal and w2 either aB or a, known as regular grammars. Regular grammars produce regular languages.
Context-Free and Regular Grammars
- Context-free grammars define the syntax of nearly all programming languages; they effectively generate a variety of languages.
- Efficient algorithms allow verification of string generation via context-free grammars.
- Regular grammars are essential in pattern searching and lexical analysis, transforming input streams to token streams for parsers.
Examples of Languages
- The language {0*^n^1^n^* | n = 0, 1, 2,...} is context-free due to productions S → 0S1 and S → λ, but not regular.
- The set {0n1n2n | n = 0, 1, 2,...} is context-sensitive, generated by a type 1 grammar, but cannot be produced by type 2 grammars.
Derivation Trees
- A derivation tree, or parse tree, graphically represents derivations in context-free languages.
- The root symbolizes the starting symbol; internal nodes are nonterminal symbols, and leaves are terminal symbols.
- Each production A → w maps the vertex representing A to children vertices that represent each symbol in w.
Parsing Approaches
- Top-Down Parsing: Begins with the start symbol, applying productions to derive a string, exemplified by deriving cbab starting from S.
- Bottom-Up Parsing: Works backward from the target string, using productions to reconstruct the derivation, demonstrating how cbab can be formed from productions to reach the starting symbol S.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
