low(S) Follow(A) Follow(B) Follow(C) Follow(D)
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I always get the wrong answer for these three, can you please provide me the correct answer for
Follow(S)
Follow(A)
Follow(B)
Follow(C)
Follow(D)
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- 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 -1For 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}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 context-free grammar G = (V, T, S, P), where V = {S, A}, T = {a, b}, and P consists of S → aSb | aAb, A → aA | λ. a. Show the derivation tree resulting from top-down parsing of the string aaaabb. b. Show the leftmost derivation of the string aaaabb.Give the derivation tree for ((a+b)∗c+d, using the grammar in Example 5.12. EXAMPLE 5.12 To rewrite the grammar in Example 5.11 we introduce new variables, taking V as {E, T, F, I}, and replacing the productions with E→T,T→F,F→I,E→E+T,T→T*F,F→(E),I→a|b|c.E→T,T→F,F→I,E→E+T,T→T*F,F→(E),I→a|b|c. A derivation tree of the sentence a + b ∗ c is shown in Figure 5.6. No other derivation tree is possible for this string: The grammar is unambiguous. It is also equivalent to the grammar in Example 5.11. It is not too hard to justify these claims in this specific instance, but, in general, the questions of whether a given context-free grammar is ambiguous or whether two given context-free grammars are equivalent are very difficult to answer. In fact, we will later show that there are no general algorithms by which these questions can always be resolved.
- 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 grammar:S →aAbB | CCA →a | CB | εB →bB | dC →aC | d | ε where S, A, B, and C are non-terminals, S is the start variable, and a, b, c, and d are terminals. Does the grammar have a predictive recursive descent parser? If the grammar has a predictive recursive descent parser, show that the conditions of predictive parsing apply for every non-terminal. On the other hand, if the grammar does not have a predictive recursive descent parser, then show ALL the conditions of predictive parsing that fail.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)
- Construct, in each case, a DFA/NFA that recognises L(G), where G is a regular grammar with productions (a) S _→ b|aS|aA, A _→ a|aA|bS. (b) S _→ aS|bS|aA, A _→ bB, B _→ aC, C _→ ε. Design NFAs and DFAs that accept the following languages: (a) a+ ∪ b∗a∗ . (b) aa∗(a ∪ b). (c) (a ∪ bb)∗(ba∗ ∪ ε). (d) (ab∗aa ∪ bba∗ab). (e) Complement of (ab ∗ aa ∪ bba∗ab). (f) (aa∗ ∪ aba∗b∗). (g) (a ∪ b)∗b(a ∪ bb)∗ . (h) (abab)∗ ∪ (aaa∗ ∪ b∗). (i) ((aa∗)∗b)∗ . (j) (ab∗a∗) ∪ ((ab)∗ba). (k) (ab∗a∗) ∩ ((ab)∗ba). (l) (a ∪ b)a∗ ∩ baa∗ . (m) (aa ∪ bb)∗(ab ∪ ba)(aa ∪ bb)∗ . (n) (aaa)∗b ∪ (aa)∗b. (o) (a(ab)∗(aa ∪ b) ∪ b(ba)∗(a ∪ bb))∗ .Question 2-Context-free Grammars Consider the alphabet = {A, V., (,), x, y, z) and the following grammar G = (V,E, R, F), defined by the rules: F (FAF) | (FVF) | (F) | P (a) Identify the set of variables and the set of terminal symbols of G. (b) Identify three words (of lengths between 10 and 20) that can be generated by the above grammar and show their derivations. (c) Consider a modified grammar G', where we remove the brackets '(' and ')' from the alphabet and the derivation rules. That is we set Σ'= {A, V., x, y, z) and we remove all occurrences of brackets in the derivation rules. Show that there are words that are derived ambiguously in G'Let G = (V, T, S, P ) be a phrase-structure grammar with V = { 0, 1, A, S }, T = { 0, 1 } and the set of productions P consisting of S →1 1S, S →2 00A, A →3 0A, A →4 0. A. Show whether 111000 ∈ L(G). B. Show whether 11001 ∈ L(G).