a. Given a grammar G =(V.T.E.P) over set of alphabets = (0....9, +. . (. ) with productions . E ->I E ->E + E E ->E E E -> (E) | -> E|0|11... 19 and derive String (9+8) (6+4) b. Languages are given as, L1 = (ab" In>=0}. L2%= L(ab"), L3=D{a,ab,abb,abbb....}, L4= (X IX is over (a,b}.begins with a, followed by any number of b. Prove that L1=L2=L3=L4
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- Construct a CFG and PDA for the language B={w| w is a string over {a,b} with the same count of a's and b's}. For example, abba € B, abab e B,aabb € B, babbbaaaba € B, that is, there is no particular order in which a's and b's appear in w as long as there is the same amount of them.FIRST set for CFG/grammar in C/C++. input is grammar , output is shown the first set. example input grammer : E -> TR R -> +T R| # T -> F Y Y -> *F Y | # F -> (E) | i Output :First(E)= { (, i, }First(R)= { +, #, }First(T)= { (, i, }First(Y)= { *, #, }First(F)= { (, i, } Assumptions : Epsilon is represented by ‘#’. Productions are of the form A=B, where ‘A’ is a single Non-Terminal and ‘B’ can be any combination of Terminals and Non- Terminals. L.H.S. of the first production rule is the start symbol. Grammar is not left recursive. Each production of a non-terminal is entered on a different line. Only Upper Case letters are Non-Terminals and everything else is a terminal. Do not use ‘!’ or ‘$’ as they are reserved for special purposes.Let ANTIPALINDROME be the language of all even-length strings over the alphabet {a,b} such that, for all i, the i-th letter from the start is different to the i-th letter from the end. Examples of strings in this language include: ε, ab, ba, aabb, abab, baba, bbaa, aaabbb, ... Give a Context-Free Grammar for the language ANTIPALINDROME.
- Create a PDA that accepts the language L = {w ∈ {a.b}* : na(v) ≥ nb(v), where v is any prefix of w}Q No. 3: Grammar G1 = ( N = { E, T, F, I, D}, T = { +, *, (, ), 0-9}, S = {E} and P is the set of productions: E E +T | T T T * F | F E) | I DI | D F I D + 0|1|2|3|4 |5 | 6 | 7 | 8 |9 For the string w = (9*(9+9)+999), find- 1. Leftmost derivation 2. Rightmost derivation 3. Parse Tree13. Show that the language L = {a" : n > 0, n # 4} is regular.
- Q4: Generate LR(0) machine for the given grammar after removing conflicts, if any? A>L L>LP |P P> (P)|()Define a common Lisp function Member-2 such that if K is a symbol and X is a list then (member-2 K X) returns T if the symbol is an element of the list, and returns NIL, if the symbol is not a element of the list. Example (member -2 'A '(C A B C D)) ==> T ( member-2 'A'(B C D)) ==> NIL Hint: you must write a common Lisp function for example, else has no predefined meaning in common Lisp and so your function must not use a COND clause of the form(else...)Make a Context free Grammar of L = {ε, uS, uSuS, uSuSuS, .........}
- Define a NPDA for the language L= {uv € {a, b}*||u|l = |v| and u # v*}. Another way to interpret L is that it is the set of all cven length strings that are not a palindrome.Using Java, a program that reads as input an arbitrary context-free grammar from a text file and then derives/enumerates five strings from the grammar. The file cfg.txt can be used to test your program. The grammar represented in cfg.txt is the following grammar for non-palindromes (from input alphabet {a,b}): S -> aSa | bSb | XX -> aYb | bYaY -> aY | bY | lambdaThis is formatted in cfg.txt as follows: S aSaS bSbS XX aYbX bYaY aYY bYY *An asterisk is used for lambda. Assume that the first state listed in the input file is the start state. Read the grammar into a map (aka hash or dictionary) where the key is a variable and the value is a list of right-hand sides. If you are using Java, you could use Hashtable by declaring a Hashtable of the following type:Hashtable<String, ArrayList<String>>Do not write the program specific to this grammar in cfg.txt. Further, assume that the test file will have more than three variables, and productions on the right hand side can…The language Balanced over E = {(,)} is defined recursively as follows 1. ЛЄ Вalanced. 2. Vx, y € Balanced, both xy and (x) are elements of Balanced. A prefix of a string x is a substring of x that occurs at the beginning of x. Prove by induction that a string x belongs to this language if and only if (iff) the statement B(x) is true. B(x): x contains equal numbers of left and right parentheses, and no prefix of x contains more right than left.