a BNF grammar that can generate nested if-else structures
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- 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>1. (a) Write the prefix form for the expression a *- ( b + c ) (b) Write an SDD for the following grammar, which converts infix expressions to prefix expressions. E -> E + T | T T -> T * F | F F -> id | (E) 2. Write the quadruples, triples, and indirect triples for the following expression - (a+b)*(c+d) - (a+b+c)Principles of programming languages: Write the BNF grammar for assignment statements written with any of the operators listed in the table below giving their precedence and associativity. The start symbol for the grammar is ASSIGN. Use the tokens ident and numlit wherever an identifier or numerical literal occurs in the appropriate rule. Note: Write your nonterminal symbols in all upper case letters. Don't use < and > in your answer since it causes problems with typing your answer. Precedence Operator Type Associativity 5 ( ) Parenthesis Left to Right 4 ! Unary logical negation Right to Left 3 == is equal to Left to Right 2 && Logical AND Left to Right 1 = %= Assignment Modulus assignment Right to Left
- 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.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 bb3. Given the following BNF grammar: -> d c | cd -> a la -> b | b Use the top-down recursive descent method which we discussed in the class to implement a parser (i.e. tdrd.parser.py) in python3 for the above BNF grammar. The input data file name is given from the command line. You may assume that there is a space character between two terminals (e.g. a a adc b ) in the data file.
- Please help with this modification:2. Use the logic in that program to design your own Recursive Descent parser in C for the following grammar:S →aABA →Abc | bB →d3. Make sure that you choose at least two strings that pass the grammar and one string that does not pass the grammar just like I did in the model program4. Submit both the code and a screen shot of your results for the choice of strings that you provided. Below is the C code that can be used to implement a Recursive Descent parser for the above grammar/* Recursive Descent Parser for the Expression Grammar:S → (L) |aL' →,SL'|εL → SL'Valid inputs: (a,(a,a)) and (a,((a,a),(a,a)))Invalid inputs:(aa,a)*/#include <stdio.h>#include <string.h>int S(), Ldash(), L();char *ip;char string[50];int main() {printf("Enter the string\n");scanf("%s", string);ip = string;printf("\n\nInput\t\tAction\n ------------------------------\n");if…14. Write a BNF grammar that describes an arbitrarily long string of the characters a, b, and c. The string can contain any number of occurrences of these three letters (including none) in any order. The strings "empty", a, accaa, abcabccba, and bbbbb are all valid members of this language.7. a. Write a BNF grammar for identifiers that consist of an arbitrarily long string of letters and digits, the first one of which must be a letter. b. Using your grammar from Exercise 7a, show a parse tree for the identifier AB5C8.
- 3. 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 -.Consider the following grammar: S➞ ACB/CbB/BaA➞ da/BCB➞ g/∈C➞ h/∈ What is the follow of B?Q1: Explain the concepts of ambiguity of a grammar. Take an example of your choice and show that the grammar is ambiguous. Draw the parse tree as needed. Q2: Select three flow control statements from C-programming, or from any other programming of your choice, and explain how the relevant grammars are written.