Consider the following two statements:
P: Every regular grammar is LL(1)
Q: Every regular set has a LR(1) grammar
Which of the following is TRUE?
P: This is false.
Every regular language is LL(1) meaning we have a LL(1) grammar for it. But we can not say same about every Regular Grammar. For example, every regular language can be represented by Left & Right Linear Grammar, where Left Linear Grammar is not LL(1), Right linear is.
Example aa* we can represent this as S>Saa which is not LL(1) ,but S>aaS is LL(1).
Q: This is true because of every LL(1) is LR(1).
All regular sets have Right recursive grammar, which is LL(1) & Every LL(1) is LR(1).
We can also say that LR(1) accepts DCFL & Regular languages are subset of DCFL.
Consider the CFG with {S,A,B) as the nonterminal alphabet, {a,b) as the terminal alphabet, S as the start symbol and the following set of production rules:
Which of the following strings is generated by the grammar?
Consider the CFG with {S,A,B) as the nonterminal alphabet, {a,b) as the terminal alphabet, S as the start symbol and the following set of production rules:
For the string aabbab , how many derivation trees are there?
Which of the following statements are true?
I. Every leftrecursive grammar can be converted to a rightrecursive grammar and viceversa
II. All ∈ productions can be removed from any contextfree grammar by suitable transformations
III. The language generated by a contextfree grammar all of whose productions are of the form (where ω , is a string of terminals and is a nonterminal), is always regular
IV. The derivation trees of strings generated by a contextfree grammar in Chomsky Normal Form are always binary trees
Statement 1 is true: Using GNF we can convert Left recursive grammar to right recursive and by using reversal of CFG and GNF we can convert right recursive to left recursive.
Statement 2 is false: because if ∊ is in the language then we can't remove ∊ production from Start symbol. (For example L = a*)
Statement 3 is true because right linear grammar generates regular set
Statement 4 is true, only two nonterminals are there in each production in CNF. So it always form a binary tree.
The grammar
For LL(1) take First(S). and do intersection between the result. if intersection is Phi then LL(1) else not.
Making a parsing table and checking if there are two or more entries under any terminal. If yes then neither LL(1) nor LR(1).
Consider an ambiguous grammar G and its disambiguated version D. Let the language recognized by the two grammars be denoted by L(G) and L(D) respectively. Which one of the following is true?
L (D) = L (G) , Both must represent same language .Also if we are converting a grammar from Ambiguous to UnAmbiguous form , we must ensure that our new new grammar represents the same language as previous grammar.
For ex G1: S>Sa/aS/a; {Ambiguous (2 parse trees for string 'aa')}
G1':S>aS/a;{Unambiguous}
Both represents language represented by regular expression: a^+
Consider these three grammars.
Which of the following statements is not true?
In G1, T can take the form of v * v * v * v * v ....
In G2, R can take the form * v * v * v ..., so T can take the form of v * v * v * v ....
Thus, in both G1 and G2, E can take the form v * v * v + v * v * v * v + v * v ....
These are the algebraic expressions involving only addition and multiplication.
In G3, T can take the form v * v * v * v, so R can take the form + v * v + v * v. Thus, through the production E ! T R, E can take the form of any arithmetic expression.
However, E can also take the form of nonarithmetic expressions,
as with E > R > + T R > + v R > + v + T R > + v + v R > + v + v.
In addition, G3 can generate ε , which G1 and G2 cannot.
Thus, while G1 and G2 generate the same language,
G3 generates a somewhat larger language. Incidentally, G1 demonstrates leftrecursion because it contains productions of the form X > X α ( in addition to nonproblematic productions of the form X > β ).
Left recursion can be eliminated by introducing a helper nonterminal R and changing the grammar to read
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