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 ______.
compilers
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.
top-down
There is another approach to this problem, called ______ parsing. In this approach, we work backward.
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Using the production S → AB shows that a complete derivation for cbab is ______.
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Which production rule is used to derive the string cbab from the non-terminal C?
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What is the first step in the top-down parsing approach for deriving cbab?
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Which production is used to replace B during the derivation of the string cbab?
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In bottom-up parsing, what is the final production rule applied to derive the string cbab from the starting symbol?
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Which approach to parsing starts with the string and works backward?
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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.
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Description
Explore the different classifications of phrase-structure grammars in this quiz. Understand the nuances of Type 0, Type 1, and Type 2 grammars, including their production rules and restrictions. Perfect for students looking to deepen their knowledge of formal language theory.
