Podcast
Questions and Answers
What is the name of the first step to convert a CFL grammar to CNF?
What is the name of the first step to convert a CFL grammar to CNF?
Arrange that all bodies of length 2 or more to consist only of variables.
What is the goal of the second step to convert a CFL grammar to Chomsky Normal Form (CNF)?
What is the goal of the second step to convert a CFL grammar to Chomsky Normal Form (CNF)?
Break bodies of length 3 or more into a cascade of productions, each with a body consisting of two variables.
What are the three preliminary simplifications for converting a context-free grammar to Chomsky Normal Form (CNF)?
What are the three preliminary simplifications for converting a context-free grammar to Chomsky Normal Form (CNF)?
- Reduce useless productions, Reduce epsilon productions, Reduce unit productions
- Eliminate empty productions, Eliminate unit productions, Eliminate useless symbols (correct)
- Eliminate useless symbols, Eliminate ε productions, Eliminate unit productions (correct)
- Eliminate ε productions, Eliminate unit productions, Eliminate Useless Symbols
- Remove useless symbols, Remove ε-productions, Remove unit productions
In the context of a grammar, unit productions are essential for generating the language.
In the context of a grammar, unit productions are essential for generating the language.
A grammar is considered to be in Chomsky Normal Form (CNF) if all productions are in the form A -> BC or A -> a, where A, B, and C are non-terminal symbols, and a is a terminal symbol.
A grammar is considered to be in Chomsky Normal Form (CNF) if all productions are in the form A -> BC or A -> a, where A, B, and C are non-terminal symbols, and a is a terminal symbol.
Describe the concept of 'generating' a symbol in the context of eliminating useless symbols.
Describe the concept of 'generating' a symbol in the context of eliminating useless symbols.
Explain the concept of 'reachable' symbol in the context of eliminating useless symbols.
Explain the concept of 'reachable' symbol in the context of eliminating useless symbols.
What is the difference between generating and reachable symbols?
What is the difference between generating and reachable symbols?
The order in which useless symbols are removed (first non-reachable, then non-generating) is crucial and cannot be reversed.
The order in which useless symbols are removed (first non-reachable, then non-generating) is crucial and cannot be reversed.
A grammar is in Chomsky Normal Form if it has no unit productions.
A grammar is in Chomsky Normal Form if it has no unit productions.
What is a unit production?
What is a unit production?
What are the final steps involved in converting a CFL grammar to Chomsky Normal Form (CNF)?
What are the final steps involved in converting a CFL grammar to Chomsky Normal Form (CNF)?
A grammar in Chomsky Normal Form (CNF) has productions only in the format A → BC or A → a.
A grammar in Chomsky Normal Form (CNF) has productions only in the format A → BC or A → a.
What is the central idea behind converting a CFL grammar to Chomsky Normal Form (CNF)?
What is the central idea behind converting a CFL grammar to Chomsky Normal Form (CNF)?
A context-free grammar is in Greibach Normal Form (GNF) if all productions are in the form A → aX, where A is a non-terminal symbol, a is a terminal symbol, and X is a sequence of (possibly empty) non-terminal symbols.
A context-free grammar is in Greibach Normal Form (GNF) if all productions are in the form A → aX, where A is a non-terminal symbol, a is a terminal symbol, and X is a sequence of (possibly empty) non-terminal symbols.
What is the key difference in format between Chomsky Normal Form (CNF) and Greibach Normal Form (GNF)?
What is the key difference in format between Chomsky Normal Form (CNF) and Greibach Normal Form (GNF)?
The Chomsky Normal Form (CNF) can be used as a starting point for the CYK parsing algorithm.
The Chomsky Normal Form (CNF) can be used as a starting point for the CYK parsing algorithm.
What is a derivation tree in the context of parsing a grammar?
What is a derivation tree in the context of parsing a grammar?
A derivation tree in a Chomsky Normal Form (CNF) grammar is a binary tree.
A derivation tree in a Chomsky Normal Form (CNF) grammar is a binary tree.
Any string of length 'n' in a grammar in Greibach Normal Form (GNF) can be derived in exactly 'n' steps.
Any string of length 'n' in a grammar in Greibach Normal Form (GNF) can be derived in exactly 'n' steps.
Grammars in normal form (CNF or GNF) can facilitate the process of proving properties related to languages generated by the grammar.
Grammars in normal form (CNF or GNF) can facilitate the process of proving properties related to languages generated by the grammar.
The Chomsky Normal Form (CNF) removes all the productions in a grammar that have ε symbols in their body.
The Chomsky Normal Form (CNF) removes all the productions in a grammar that have ε symbols in their body.
Flashcards
String
String
A sequence of characters, often used to represent text or code.
Grammar
Grammar
A formal system that defines the syntax of a language.
Context-free grammar (CFG)
Context-free grammar (CFG)
A grammar is context-free if the left-hand side of each production rule consists of a single non-terminal symbol.
Nullable variable
Nullable variable
A non-terminal symbol that can derive the empty string (ε).
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Unit production
Unit production
A production rule of the form A → B, where both A and B are non-terminal symbols.
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Chomsky Normal Form (CNF)
Chomsky Normal Form (CNF)
A grammar where the productions are of the form A → BC or A → α, where A, B, and C are non-terminal symbols, and α is a terminal symbol.
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Greibach Normal Form (GNF)
Greibach Normal Form (GNF)
A grammar where the productions are of the form A → αX, where A is a non-terminal symbol, α is a terminal symbol, and X is a sequence of (possibly empty) non-terminal symbols.
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Reachable symbol
Reachable symbol
A non-terminal symbol that can be derived from the start symbol. It can be reached in the derivation.
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Generating symbol
Generating symbol
A non-terminal symbol that can derive a string of terminal symbols. It can produce actual text.
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Useful symbol
Useful symbol
A symbol that is both reachable and generating.
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Eliminate non-generating symbols
Eliminate non-generating symbols
A process of removing non-generating symbols from a grammar.
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Eliminate non-reachable symbols
Eliminate non-reachable symbols
A process of removing non-reachable symbols from a grammar.
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Eliminate ε productions
Eliminate ε productions
A process of eliminating production rules that contain the empty string (ε) as the right-hand side.
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Start symbol standardization
Start symbol standardization
A process of transforming grammar rules to ensure that only the designated start symbol can produce a string of terminal symbols.
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Terminal symbol standardization
Terminal symbol standardization
A process of transforming grammar rules to ensure that all terminal symbols appear only in the right-hand side of production rules.
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Eliminate unit productions
Eliminate unit productions
A process of removing production rules of the form A→B where both A and B are non-terminal symbols.
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Body decomposition
Body decomposition
Creating new non-terminal symbols and production rules to break down longer production bodies.
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Terminal extraction
Terminal extraction
Replacing terminal symbols within long production bodies with new non-terminal symbols that have single production rules producing the original terminal.
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Eliminate left-recursion
Eliminate left-recursion
A process of removing left-recursive productions from a grammar.
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Derivation
Derivation
A notation used to describe the process of deriving strings in a formal language using a grammar.
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Derivation tree
Derivation tree
A tree-like structure that represents the derivation of a string in a formal language.
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Formal language theory
Formal language theory
A branch of computer science that deals with formal systems for describing and analyzing languages.
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Conversion to Chomsky Normal Form
Conversion to Chomsky Normal Form
A process of converting a context-free grammar into an equivalent grammar in Chomsky Normal Form.
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Conversion to Greibach Normal Form
Conversion to Greibach Normal Form
A process of converting a context-free grammar into an equivalent grammar in Greibach Normal Form.
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Rule combination
Rule combination
The process of combining multiple production rules for a particular non-terminal symbol into a single rule.
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Grammar optimization
Grammar optimization
A process of optimizing a grammar by removing redundant rules or symbols.
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Grammar verification
Grammar verification
A process of testing a grammar for correctness and completeness.
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Grammar rules
Grammar rules
A set of production rules that define the structure of a formal language.
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CSE322 Normal Forms: CNF & GNF
- The lecture covers Chomsky Normal Form (CNF) and Greibach Normal Form (GNF) for context-free grammars.
- A presentation outline includes introduction, Chomsky normal form, preliminary simplifications, final steps, Greibach Normal Form, algorithm example, and summary.
- A grammar is defined as G = (V, T, P, S), where:
- V is a set of variables.
- T is a set of terminals.
- P is a set of productions.
- S is the start symbol.
- An example grammar is provided, with terminals T = {a, b}, variables V = {A, B, C}, start symbol S, and production P = S → A.
- A grammar example illustrates how a grammar generates strings, such as L = {anbncn | n ≥ 1}.
- Context-free grammar: the head of any production contains only one non-terminal symbol. -Example S→P; P→aPb; P→ε; L = {anbn | n ≥ 0}
- Chomsky Normal Form: all productions are either A → BC or A → a, where A, B, and C are non-terminal symbols and a is a terminal symbol.
- Preliminary simplifications for CNF include eliminating useless symbols, ε productions, and unit productions.
- Useless symbols are identified by generating and reachable symbols. A symbol is generating if it can derive a terminal string. A symbol is reachable if it can be derived from the start symbol.
- ε productions are productions that produce the empty string.
- Create two versions of the production, one with the nullable variable and one without.
- Eliminate productions with empty bodies.
- Unit productions are productions of the form A → B where A and B are variables.
- Identify unit pairs
- Replace every occurrence of B with ω.
- Steps to convert a grammar to CNF:
- Arrange all bodies of length 2 or more to consist only of variables.
- Break bodies of length 3 or more into a cascade of productions, each with a body consisting of two variables.
- Greibach Normal Form: all productions are of the form A → aX, where A is a non-terminal symbol, a is a terminal symbol, and X is a sequence of non-terminal symbols (possibly empty).
- Example of removing non-generating and non-reachable symbols are given.
- Steps for finding generating and reachable symbols.
- Examples for ε productions and unit productions are shown.
- Summary of the properties of CNF and GNF, including how derivation trees are structured, how string lengths relate to derivation steps, and how normal forms facilitate proofs.
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