Which of the following must be finite and which may be infinite?
Homework Answers
Solution:
(a)
The language generated by a regular grammar may be infinite.
Explanation: Regular grammar can generate finite language as well as infinite also so in some cases it can also generate infinite language so the answer will be that the language generated by a regular grammar may be infinite.
For example (a+b)* is a regular expression and the
language L ={
,a,b,aa,bb,ab,ba........}
so this language is infinite.
(b)
The set of nonterminals in regular grammar is always finite.
Explanation: When we define some regular grammar then we have some set of terminals, nonterminals and set of productions.
Nonterminals are the generating symbols that are generally written on the left side of productions.
Example: A -> a/b (production rule) here A is nonterminal and {a,b} are set of terminals .
(c)
The number of regular grammars that generates a given set of strings may be infinite.
Explanation: There may be an infinite number of regular grammar that can produce the same set of strings and the structure of regular grammar can be different.
(d)
The length of a derivation based on a regular grammar may be infinite.
Explanation: When we are generating an infinite length string from the set of productions for the given grammar in that case when we try to produce the string through derivation then the length of derivation may be infinite.
(e)
The number of terminal symbols in regular grammars are always finite.
Explanation: When we define some regular grammar then we have some set of terminals, nonterminals and set of productions.
terminals are always written on the right side of productions.
Example: A -> a/b (production) here A is nonterminal and {a,b} are set of terminals so basically number of terminals are always finite for the given grammars.
(f)
The number of productions in regular grammar is always finite.
Explanation: When we define some regular grammar then we have some set of terminals, nonterminals, set of productions.
A production contains a set of terminals and nonterminals.
A -> Aa/b (Production rule) so in any regular grammar number of productions are always finite.
(g)
The length of string generated by a regular grammar may be infinite.
Explanation: Regular grammar can generate finite-length strings as well as infinite length string.
For example (a+b)* is a regular expression and the
language L ={,a,b,aa,bb,ab,ba........}
there will be many strings of infinite lengths.
Add Answer to:
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I could say "C generates binary strings of length one, E
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strings. If the grammar has more than one variable, we will ask to
write a sentence describing what sets of strings expect each
variable in the grammar to generate. For example, if the grammar
was:
I could say "C generates binary strings of length one, E
generates (non-empty) even length binary strings, and O generates
odd length binary strings." It is also fine to use a regular
expression, rather than English,...
Construct context-free grammars that generate the given set of
strings. If the grammar has more than one variable, we will ask to
write a sentence describing what sets of strings expect each
variable in the grammar to generate. For example, if the grammar
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I could say "C generates binary strings of length one, E
generates (non-empty) even length binary strings, and O generates
odd length binary strings." It is also fine to use a regular
expression, rather than English,...
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