1. Fill in the ??? Part of grammar G = (???) based on the productions. Guess what're S and D stand for? (1) S→ for (i = D to D) c (2) D→ dDId where it is an identifier, d is a digit, c represents some statements
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- a. Eliminate Left Factoring from the grammar above. b. Eliminate Left Recursive from the grammar above if there is any.1.Eliminate left recursion from the production rules that are given in below. E = E + T / T 2.Define context-free grammar. 3.Write down the characteristic of context-free grammar.Give context free grammar for the following :
- Problem 1: Write a regular expression that recognizes the following language over the alphabet {a,b}: Any string containing the letters a and b, where the number of letters is not a multiple of three. (Note that 0 is a multiple of three.) Your regular expression should contain only a and b, and the metacharacters (, ), *, +, ? and |. Problem 2: Write a context free grammar that recognizes language from Problem 1. Your start symbol should be named S.Write a grammar for Boolean expressions , assuming that we already have rules in our grammar for arithmetic expressions . Arithmetic expressions might be simple literals like 3 or 97 or may be more complex syntactic units like (3+x)/4. They evaluate to a number. You needn't concern yourself with their structure; just that they can be used as below. Boolean expressions include the literals TRUE and FALSE; they can be combined with the unary operator ! (meaning NOT) and binary operators && and || (meaning AND and OR). Also, arithmetic expressions can be combined with the following binary operators to form new Boolean expressions: , =, !=. When your grammar is complete, you should be able to derive parse trees for expressions like the following: TRUE || FALSE FALSE && !TRUE 27 = TRUE | FALSE3. Write a correct recursive descent grammar that correctly recognizes arithmetic expressions involving variable, number, + - * / **. Variable and number are tokens recognized by the lexical analyzer along with the operators + - * / and **. There are three levels of hierarchy, ** before *, / before + -. This grammar does not support unary + and -.
- d) Construct a type-3 grammar that derives the L₂ language. (You can use the A- intransitive diagram you found in b.) 5. Let the G, grammar be defined as follows: QILIAH Блязадоля до УТИБАЯ TO G₁VN,VT.P.S> UDAL VN: (S, A, B, CADA ESOSESOE VT: (0,1) P: SOS | 1A A OBAM B➡ OB | 15 | 1 H odmuinsbur2. a) What type of grammar is G₁? b) Construct the FA (finite automaton) model that recognizes the language derived from this grammar and draw the transition diagram.. HOITUDWrite a grammar for the language consisting of strings built only of theletters aand b. The strings may have any number of these letters, but the letter combinationsbabmust be in each stringsomewhere, and each stringmust startwithabb. For example, the strings bbababbbaa, bbbaaaababaa, and bbbabare in the language, whilea, aabb, baaa, and bbba are not.1. Use the algorithm described in class that takes a CFG and converts it into a CNF (Chomsky Normal Form) grammar that generates the same language as the original grammar, except possibly for the string A, to answer the following question. As part of your answer, you should say which variables are nullable, and you should give the appropriate grammar after each step of the algorithm. There are four steps. Give a CFG (context-free grammar) in CNF (Chomsky Normal Form) that generates the same language, except possibly for the string A, as the following grammar: SAB AB →bAa A → aaB bb
- a. Write a BNF grammar for the language consisting of strings built only of the letters a and b. The strings may have any number of these letters, but the letter combinations bb must be in each string somewhere, and each string must start with a aa. For example, the strings aaabbabbba, aaaababba, and aababbabb are in the language, while a, bba, ababb, aabaa, and bbaa are not. b. Draw the parse tree for string aabbaaba according to the previous grammar: c. Describe, in complete English sentences and “layman’s terms,” the language defined by the following grammar in BNF (start symbol is <S> ): <S>::= <A>a|<B>b <C>::= c <A>::= a<A>a|<C> <B>::= b<B>b|<C>24. Suppose that you are defining a grammar for scientific notation numbers. (Ex: "1.3e+5"). What are supposed to be the terminals in this language? (Tip: try to use a float point representation using regular expression).A) Write a BNF grammar for the language consisting of strings built only of the letters a and b. The strings may have any number of these letters, but the letter combinations bb must be in each string somewhere, and each string must start with a aa. For example, the strings aaabbabbba, aaaababba, and aababbabb are in the language, while a, bba, ababb, aabaa, and bbaa are not. B) Draw the parse tree for string aabbaaba according to the previous grammar: C) Describe, in complete English sentences and “layman’s terms,” the language defined by the following grammar in BNF (start symbol is <S>):<S> ::= <A>a | <B>b<C> ::= c<A> ::= a<A>a | <C><B> ::= b<B>b | <C>