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2. Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9. A → BAB | B& B → 00 | E

2. Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9. A → BAB | B& B → 00 | E

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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DEFINITION 2.8 A context-free grammar is in Chomsky normal form if every rule is of the form A → BC A → a where a is any terminal and A, B, and C are any variables-except that B and C may not be the start variable. In addition, we permit the rule Se, where S is the start variable. Example SASA aB A BS B→ be So → S S → ASA | aB ABIS B → be So S SASA | aBa|SA|AS| S ABS B-b So ASA| aBa|SA| AS SASA aBa|SA| AS ABS b B-b So S SASA aB a ABSC B-be A₁ So SASA | aBa|SA| AS SASA aBa|SA| AS A → B|S B-b So ASA aBa|SA| AS SASA aBa| SA AS A → Sb ASA | aBa|SA| AS B-b So AA₁ |UB|a|SA| AS SAA₁ |UB|a|SA| AS Ab AA₁ |UB|a|SA| AS SA U → a B→ b So S SASA | aBa|SA|AS| S A → B Se B-b
Transcribed Image Text:DEFINITION 2.8 A context-free grammar is in Chomsky normal form if every rule is of the form A → BC A → a where a is any terminal and A, B, and C are any variables-except that B and C may not be the start variable. In addition, we permit the rule Se, where S is the start variable. Example SASA aB A BS B→ be So → S S → ASA | aB ABIS B → be So S SASA | aBa|SA|AS| S ABS B-b So ASA| aBa|SA| AS SASA aBa|SA| AS ABS b B-b So S SASA aB a ABSC B-be A₁ So SASA | aBa|SA| AS SASA aBa|SA| AS A → B|S B-b So ASA aBa|SA| AS SASA aBa| SA AS A → Sb ASA | aBa|SA| AS B-b So AA₁ |UB|a|SA| AS SAA₁ |UB|a|SA| AS Ab AA₁ |UB|a|SA| AS SA U → a B→ b So S SASA | aBa|SA|AS| S A → B Se B-b
2. Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9. A → BAB | B & B → 00 | E
Transcribed Image Text:2. Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9. A → BAB | B & B → 00 | E
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