The Context Free Grammar below is given: G=( {S,a,b}, {0,1}, S, {S⇒0b|1a, a→0|0s|1aa|ɛ, b→1|1s|Obb}) Which string(s) could belong to the language generated by this grammar? 101110111 ☐ 10010100 0100101110 0000100001
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- 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 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 -1Consider 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
- Regular grammar, S ⟶⟶ aS | bS |a | bb, will generate the following language L: Group of answer choices: A)L = L ((a +b)* (a + bbb)) b)L = L ( a(a + b)*bb) c)L = L ( (bb + a) (a + b)*) D)L = L ((a + b)* (a + bb))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/Give a context-free grammar generating the following language over the alphabet {a, b,#}: *Check uploaded image*
- Can you describe an algorithm that given two context-free grammars G1 and G2 outputs YES if andonly if every string generated by G1 is also generated by G2. (I.e., output YES exactlywhen the set of strings generated by G1 is a subset of the set of strings generated by G2.)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 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.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)
- Consider the grammarS ⟶⟶ aSc |S1S1 ⟶⟶ b S1cc |?λThis grammar will generate the following language L. Group of answer choices: a)None of the rest b)L = {anbmck : n+2m = k} c)L = {anbmck : n+3m = k}For each of these languages, give both a context-free grammar and a push down automaton. Briefly explain how your CFG and PDA work. Your CFG should be relatively simple and contain at most 6 variables. For this question, your PDA cannot be directly convertedfrom your CFG (a)L1={ x#y | x is a prefix of yR, and y∈{a,b}* } ,Σ ={a,b,#} Recall that wR is w written backwards, and u is a prefix of v if v=ut for some stringt.For example bb#abb is in L1, but a#ab is not. (b)L2={ aibjck | i ≥ j or j ≥ k } (c)L3 = {w∈{a,b}* | w contains an unequal number of a’s and b’s}Formal Languages and Automata Theory Give context-free grammars that generate the following languages. In all parts, thealphabet Σ is {0,1} a. {w| w contains at least three 1s}b. {w| w starts and ends with the same symbol}c. {w| the length of w is odd}Ad. {w| the length of w is odd and its middle symbol is a 0}e. {w| w = wR, that is, w is a palindrome}f. The empty set