The exercises of Chapter Three3.2 Given the grammar AAA|(A)|a. Describe the language it generates; b. Show that it is ambiguous. Solution: a. Generates a string of balanced parenthesis, including the empty string. b. parse trees of ():3.3 Given the grammar exp exp addop term | term addop + | - term term mulop factor| factor mulop * factor ( exp ) | number Write down leftmost derivations, parse trees, and abstract syntax trees for the following expression: a. 3+4*5-6b. 3*(4-5+6)c. 3-(4+5*6) Solution:a.The leftmost derivations for the expression 3+4*5-6:Exp = exp addop term =exp addop term addop term =term addop term addop term= factor addop term addop term=3 addop term addop term = 3 + term addop term=3+term mulop factor addop term =3+factor mulop factor addop term=3+4 mulop factor addop term = 3+4* factor addop termA()AAAAA()=3+4*5 addop term = 3+4*5-term= 3+4*5-factor=3+4*5-63.5 Write a grammar for Boolean expressions that includes the constants true and false, the operators and, or and not, and parentheses. Be sure to give or a lower precedence than and and and a lower precedence that not and to allow repeated nots, as in the Boolean expression not not true. Also be sre your grammar is not ambiguous. solutionbexpbexp or A | AA A and B | B B not B | C C (bexp) | true | falseEx: not not true boolExp A B not B not not B not not C not not true 3.8 Given the following grammar statementif-stmt | other | if-stmt if ( exp ) statement else-partelse-part else statement | exp 0 | 1 a. Draw a parse tree for the string if(0) if (1) other else else otherb. what is the purpose of the two elses? The two elses allow the programmer to associate an else clause with the outmost else, when two if statements are nested and the first does not have an else clause. c. Is similar code permissible in C? Explain. The grammar in C looks like: if-stmtif ( exp ) statement | if (exp) statement else statement the way to override “dangling else” problem is to enclose the inner if statement in s. e.g. if (0) if(1) other else other.3.10 a. Translate the grammar of exercise 3.6 into EBNF.b. Draw syntax diagramms for the EBNF of part (a). Solution a. The original grammarlexp atom|listatomnumber|identifierlist (lexp-seq)lexp-seq lexp-seq lexp| lexpThe EBNF of the above grammar:lexp atom|listatomnumber|identifierlist (lexp-seq)lexp-seq lexp lexpb. The syntax diagramms for the above EBNF:lexpatomlistlexp-seq3.12. Unary minuses can be added in several ways to the simple arithmetic expression grammar of Exercise 3.3. Revise the BNF for each of the cases that follow so that it satisfies the stated rule. a. At most one unary minus is allowed in each expression, and it must come at the beginning of an expression, so -2-3 is legal ( and evaluates to -5 ) and -2-(-3) is legal, but -2-3 is not. exp exp addop term | term addop + | - term term mulop factor| factoratomlistNUMIDE(lexp-seq)lexplexpmulop * factor ( exp ) | (-exp) | number | b. At most one unary minus are allowed before a number or left parenthesis, so -2-3 is legal but -2 and -2-3 are not. exp exp addop term | term addop + | - term term mulop factor| factor mulop * factor ( exp ) | -(exp) | number | -number c. Arbitrarily many unary minuses are allowed before numbers and left parentheses, so everything above is legal. 3.19 In some languages ( Modula-2 and Ada are examples), a procedure declaration is expected to be terminated by syntax that includes the name of the procedure. For example, in Modular-2 a procedure is declared as follows: PROCEDURE P; BEGIN END P; Note the use of the procedure name P alter the closing END. Can such a requirement be checked by a parser? Explain. Answer This requirement can not be handled as part of the grammar without making a new rule for each legal variable name, which makes it intractable for all practical purposes, even if variable names are restricted to a very short length. The parser will just check the structure, that an identifier follows the keyword PROCEDURE and an identifier also follows the keyword END, however checking that it is the same identifier is left for semantic analysis. See the discussion on pages 131-132 of your text. 3.20 a. Write a regular expression that generate the same language as the following grammar:A aA|B|B bB|Ab. Write a grammar that generates the same language as the following regular expression:(a|c|ba|bc)*(b|)Solution a. The regular expression:(a|b)* b. The grammar: Step 1:A BCBaB|cB|baB|bcB|Cb|Step 2:A Bb|BBaB|cB|baB|bcB|