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See the image. a.Construct a context-free grammar generating C.Explain how your construction accounts for each rule

See the image. a.Construct a context-free grammar generating C.Explain how your construction accounts for each rule

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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See the image.

a.Construct a context-free grammar generating C.Explain how your construction accounts for each rule.

b.We could eliminate one rule from Cand make it regular. Which rule would that be, and why would it work? You do not need a formal proof, but you do need an explanation.

Let C be the language over {a, b, c, d, e, f} accepting all strings so that: 1. There are precisely two b's in the string. 2. Every a is immediately followed by an odd number of e's. 3. Every d is immediately followed by an even number of f's. 4. e's and f's don't occur except as provided in rules 2 and 3. 5. All a's occur after the first b. 6. All d's occur before the second b. 7. In between the two b's there are exactly twice as many a's as d's. HINT: Don't be intimidated by the number of rules. The way they interact actually helps you simplify the number of cases you have to deal with while constructing this grammar.
Transcribed Image Text:Let C be the language over {a, b, c, d, e, f} accepting all strings so that: 1. There are precisely two b's in the string. 2. Every a is immediately followed by an odd number of e's. 3. Every d is immediately followed by an even number of f's. 4. e's and f's don't occur except as provided in rules 2 and 3. 5. All a's occur after the first b. 6. All d's occur before the second b. 7. In between the two b's there are exactly twice as many a's as d's. HINT: Don't be intimidated by the number of rules. The way they interact actually helps you simplify the number of cases you have to deal with while constructing this grammar.
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