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. A DG is said to be in Chomsky Form (CNF), if all the productions are of the form A -> BC or A -> a . Let G be a CFG in CNF. To derive a string of terminals of length x, the number of productions to be used is
(a) 2x - 1
(b) 2x
(c) 2x + 1
(d) 2x?
(a) 2x - 1
(b) 2x
(c) 2x + 1
(d) 2x?
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. A DG is said to be in Chomsky Form (CNF), if all the productions are...
Understanding Chomsky Normal Form (CNF)
A Context-Free Grammar (CFG) is in Chomsky Normal Form (CNF) if all its production rules follow these two forms:
- A -> BC (where A is a non-terminal and B, C are non-terminals)
- A -> a (where A is a non-terminal and a is a terminal symbol)
Productions for String Derivation
To derive a string of terminals of length x in CNF, we need to analyze how many productions are required:
- Each terminal symbol in the string requires a production of the form A -> a. Thus, for x terminal symbols, we need x productions of this type.
Combining Non-Terminals
- To construct a string of x terminal symbols, we must also consider how to combine the non-terminals that will eventually lead to these terminals.
- For each production of the form A -> BC, we create a new non-terminal. To create x terminal symbols, we need to produce x - 1 non-terminals (since we start from a single non-terminal).
Total Productions Calculation
- Therefore, the total number of productions required is:
- x productions for the terminals (A -> a)
- (x - 1) productions for combining non-terminals (A -> BC)
- Summing these gives us: x + (x - 1) = 2x - 1
Conclusion
Thus, the number of productions required to derive a string of terminals of length x in CNF is:
- (a) 2x - 1
This understanding is crucial for working with CFGs in Chomsky Normal Form and analyzing their derivation processes effectively.
A Context-Free Grammar (CFG) is in Chomsky Normal Form (CNF) if all its production rules follow these two forms:
- A -> BC (where A is a non-terminal and B, C are non-terminals)
- A -> a (where A is a non-terminal and a is a terminal symbol)
Productions for String Derivation
To derive a string of terminals of length x in CNF, we need to analyze how many productions are required:
- Each terminal symbol in the string requires a production of the form A -> a. Thus, for x terminal symbols, we need x productions of this type.
Combining Non-Terminals
- To construct a string of x terminal symbols, we must also consider how to combine the non-terminals that will eventually lead to these terminals.
- For each production of the form A -> BC, we create a new non-terminal. To create x terminal symbols, we need to produce x - 1 non-terminals (since we start from a single non-terminal).
Total Productions Calculation
- Therefore, the total number of productions required is:
- x productions for the terminals (A -> a)
- (x - 1) productions for combining non-terminals (A -> BC)
- Summing these gives us: x + (x - 1) = 2x - 1
Conclusion
Thus, the number of productions required to derive a string of terminals of length x in CNF is:
- (a) 2x - 1
This understanding is crucial for working with CFGs in Chomsky Normal Form and analyzing their derivation processes effectively.
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. A DG is said to be in Chomsky Form (CNF), if all the productions are of the form A -> BC or A -> a . Let G be a CFG in CNF. To derive a string of terminals of length x, the number of productions to be used is(a) 2x - 1(b) 2x(c) 2x + 1(d) 2x?
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. A DG is said to be in Chomsky Form (CNF), if all the productions are of the form A -> BC or A -> a . Let G be a CFG in CNF. To derive a string of terminals of length x, the number of productions to be used is(a) 2x - 1(b) 2x(c) 2x + 1(d) 2x? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about . A DG is said to be in Chomsky Form (CNF), if all the productions are of the form A -> BC or A -> a . Let G be a CFG in CNF. To derive a string of terminals of length x, the number of productions to be used is(a) 2x - 1(b) 2x(c) 2x + 1(d) 2x? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . A DG is said to be in Chomsky Form (CNF), if all the productions are of the form A -> BC or A -> a . Let G be a CFG in CNF. To derive a string of terminals of length x, the number of productions to be used is(a) 2x - 1(b) 2x(c) 2x + 1(d) 2x?.
. A DG is said to be in Chomsky Form (CNF), if all the productions are of the form A -> BC or A -> a . Let G be a CFG in CNF. To derive a string of terminals of length x, the number of productions to be used is(a) 2x - 1(b) 2x(c) 2x + 1(d) 2x? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about . A DG is said to be in Chomsky Form (CNF), if all the productions are of the form A -> BC or A -> a . Let G be a CFG in CNF. To derive a string of terminals of length x, the number of productions to be used is(a) 2x - 1(b) 2x(c) 2x + 1(d) 2x? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . A DG is said to be in Chomsky Form (CNF), if all the productions are of the form A -> BC or A -> a . Let G be a CFG in CNF. To derive a string of terminals of length x, the number of productions to be used is(a) 2x - 1(b) 2x(c) 2x + 1(d) 2x?.
Solutions for . A DG is said to be in Chomsky Form (CNF), if all the productions are of the form A -> BC or A -> a . Let G be a CFG in CNF. To derive a string of terminals of length x, the number of productions to be used is(a) 2x - 1(b) 2x(c) 2x + 1(d) 2x? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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