Which one(s) of the following Context Free Grammars would be in the form of Greibach Normal Form? G=( {S,A,B}, {a,b}, S, {S BB|b, A B→a|SA}) a|b|SS, ☐ G=( {S,A,B}, {a,b}, S, {SaAlb, A⇒a|b|bABSS, B→a|SA}) ☐ G=( {S,a,b}, {0,1}, S, {S Oab|1, a b―0|0Sa}) 0|1bSS, G=( {S,a,b}, {0,1}, S, {S→0ab|1, a→0|bSS, b―0|0S})
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- L = {(a^n)(b^m)(c^k) ; n = m or m ≠ k } Find context free grammars (with n, m, k greater than or equal to 0)Assumptions ... Alphabet = {a, b} • L1 = { a"b" : n ≥ 0 ^ n mod 3 = 0} L2 = {anbm : n ≥ 0 ^ m ≥ 0 ^ n = m −1} To do in this exercise ... ⚫ Find a context-free grammar G such that L(G) = L1 L2, the concatenation of languages L1 and L2. ⚫ Save your context-free grammar as a JFLAP.jff file, and submit that .jff file to Canvas as your solution to th is exercise.Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s and b’s, and the set of b’s is consecutive in the string, e.g., ab, abba, aabb, abbbaa, aaabbbbbaa, etc. Note that ε ∈ L for completeness (0 number of a’s is equal to 0 number of b’s, which are also consecutive). Show that this language is context-free by giving a context-free grammar. Please make sure to test the answers onhttps://web.stanford.edu/class/archive/cs/cs103/cs103.1156/tools/cfg/
- Consider the context-free grammar S → ASA | AA → aA | ab When following the CFG-to-PDA conversion process learned in class, there is only one state in the resulting PDA that has a self-loop. Of all the PDA triples on this self-loop, write the shortest one that contains an "a" or a "b" anywhere in the triple in the box below (if there is more than one shortest, write any of them).Consider the following grammar: <S> à <A> a < B> b <A> à <A> b | b <B> à a <B> | a Which of the following sentences are in the language generated by this grammar? baab bbbab bbaaaaaS bbaabConsider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a's and b's, and the set of b's is consecutive in the string, e.g., ab, abba, aabb, abbbaa, aaabbbbbaa, etc. Note that ɛ € L for completeness (0 number of a's is equal to 0 number of b's, which are also consecutive). Show that this language is context-free by giving a context-free grammar.
- Grammar and its application to FractalsLet G=(N,T,P,∑) where ∑ is the start symbol, N = {D}, T = {d, r, l}, andP = {∑→D, D→DrDllDrD, D → d} 1. Give the most specific type of grammar G.2. Show the leftmost derivation sequence of the string drdlldrd, (i.e. When deriving a new sentential form, always replace one Nonterminal at a time and always replace the leftmost Nonterminal)3. Suppose d is an abstraction of a command to draw a straight line of fixed length in the current direction, r is an abstraction of a command to turn right by 60 degrees, and l is an abstraction of a command to turn left by 60 degrees. Assuming that you are to start from a point and that the starting direction is to proceed horizontally to the right, show the figure represented by the generated string drdlldrd.4. The string drdlldrdrdrdlldrdlldrdlldrdrdrdlldrd can also be generated. Assuming that you are to start from a point and that the starting direction is to proceed horizontally to the right, show the figure…Consider the following context-free grammar:G = (N, Σ, P, S)N = {S, T}Σ = {a, b, c}Productions in P are:S →aSaS →TT →bTT →TcT →ε(4.a) Write down a derivation of the string abbca from the grammar G.(4.b) Draw a parse tree corresponding to the derivation from part a).(4.c) Is the grammar G ambiguous? Explain your answer.Consider the grammar G below in the input alphabet {x, y, z, *}, with leading non-terminal S' in rule 1. S'→S $ S → E * F S → F E → x E → z F y F F → E a) Build the LR(1) automaton of grammar G. Is this grammar LR(1)? b) List the LR(1) items in the last automaton state reached (without performing reductions on the last character) when the input is: x* z zx zxy For this question, indicate the lookahead and the top of the stack, it is also necessary to list the states in the same order as the grammar rules. Also, list the lookaheads in the order {?, $, x, y, z, *} c) Check if G is LALR. If so, answer with the number of states eliminated in relation to the previous automaton. If not, answer with -1
- Here we concern the following given context-free grammar for generating email addresses. A → N@id.N N → N.id | id Some email addresses examples are: id@id.id id.id@id.id id.id@id.id.id id.id.id@id.id.id.id Remove all left recursions in the above given grammar. Please determine the FIRST and FOLLOW sets for all nonterminals in the revised grammar in (1). Using your results from (2), construct the LL(1) parsing table for your updated grammar in (1). To save your time, a part of table is provided with column labels. You will need to provide the necessary row labels and corresponding table entries.Consider the context-free grammar S → ABS | ABA → aA | aB → bB | b Give a leftmost derivation of the string "abab". Your derivations should begin with S, end with abab, and only make one substitution per step. Do not include any spaces, quotes, or lambdas in your answer. Use the ">" character to represent the right arrow. For example, S>aSb>ab might be a legal derivation for a string in another language. Hints: > should appear six times in your answer.Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s and b’s, and the set of b’s is consecutive in the string, e.g., ab, abba, aabb, abbbaa, aaabbbbbaa, etc. Note that ε ∈ L for completeness (0 number of a’s is equal to 0 number of b’s, which are also consecutive). Show that this language is context-free by giving a context-free grammar. I want a CFG