A grammar is a 4-tuple G, G = (Ν, Σ, Π, Σ, S) where, Ν is a finite set of nonterminal symbols, Σ is a finite set of terminal symbols, Π is a finite set of rules,S is the starting symbol.
Let, Ν = {S, T}
Σ = {a, b, c}
Π = {
S -> aTb
S -> ab
aT -> aaTb
aT -> ac
} S is the starting symbol.
A) Prove that the given grammar G is a context sensitive grammar.
B) What is the language L = L(G) generated by the given grammar G?
C) For the string aaacbbb design the appropriate syntax tree based on the context sensitive grammar G.
D) The language L = L(G) generated by the given grammar G is also context free language. Write the context free grammar G1 that generates the language L.
E) For the string aaacbbb design the appropriate syntax tree based on the context free grammar G1.
Automata: solve a - e 2. (10+10+10+10+10-50 points) Agrammar is a 4-tuple G, G-ON,E,11,L$) where N is a finite set of nonterminal symbols Σ is a finite set of terminal symbols is a finite set of rules S is the starting symbol Let N- (S, T s-{a, b, c} s-> ab aT >aaTb aT-ac S is the starting symbol. (a 10 points) Prove that the given grammar G is a context sensitive grammar. (b-10 points) What is the language L-...
Theory of Computation 7. Write down the Chomsky Normal Form for the context-free language de- fined by the productions: S bAļaB. A bAA laSla, and B aBB bS b, where S, A, B are nonterminal symbols and a, b are terminal symbol 8. For the context-free grammar Ģ -(X, T, R, S) with X (A, B. C, a, b), T a, b and productions R: SAB |BC, ABAa, BCClb,C AB la, check by applying the CYK Theorem whether the string...
1. Consider the following grammar A - aB B-Sb (a) Show a derivation tree for the string aabbbb using the grammar. (b) Give an English description of the language generated by the grammar 2. Let G be the grammar below: S-ASB ab | SS (a) Show that G is ambiguous. (b) Construct an unambiguous grammar equivalent to G. 3. Find a context free grammar for the language L3- fa"b"c+m :n,m21) 4. Find a context free grammar for the language L4...
4. Consider the following context-free grammar S SSSS a (a) Show how the string aa+a* can be generated by this grammar (b) What language does this grammar generate? Explain
Consider the following context-free grammar with terminals {a, b, c, d} and start symbol S. S → W | X | Y | Z W → AW D | X | Y | Z X → BXD | Z Y → AY C | Z Z → BZC | ε A → a B → b C → c D → d (a) Give a derivation tree with input string: aaaabccddd (b) What language does this CFG recognize? Give a...
Automata and Computability Problems Please check my work. Make necessary edits/corrections to my work. Please add more detail to number 2 for better understanding :) 1. Give a context-free grammar (CFG) for each of the following languages over the alphabet = (a, b): (a) All nonempty strings that start and end with the same symbol. 2. Answer each part for the following context-free grammar. I. II. III. IV. V. R> XRXS S -ать | bТа T → XTX | X...
formal language automata 1. (15p) Consider the Context-free grammar G defined by: S → 0A1A1A1A A0A1A a) Describe L(G). (5p) b) Convert G into a Pushdown Automaton (PDA). (10p)
3 points) Question Three Consider the context-free grammar S >SS+1 SS 1a and the string aa Give a leftmost derivation for the string. 3 points) (4 poiots) (5 points) (3 points) sECTION IWOLAttcmpt.any 3.(or 2) questions from this.scction Suppose we have two tokens: (1) the keyword if, and (2) id-entifiers, which are strings of letters other than if. Show the DFA for these tokens. Give a nightmost derivation for the string. Give a parse tree for the string i) Is...
discrete mathematics Leavening question 4 solve others 4. Let be the automaton with the following input set A, state set S and accepting or final ("yes") state set F : A-t, b },s-b"11":2},7-bl } . Suppose s, is the initial state of M , and next state function F of M is given by the table B. Draw the state diagram D D() of the automaton 4 5. Construct the state diagram for the finite-state machine with the state table...
If L1 and L2 are Regular Languages, then L1 ∪ L2 is a CFL. Group of answer choices True False Flag this Question Question 61 pts If L1 and L2 are CFLs, then L1 ∩ L2 and L1 ∪ L2 are CFLs. Group of answer choices True False Flag this Question Question 71 pts The regular expression ((ac*)a*)* = ((aa*)c*)*. Group of answer choices True False Flag this Question Question 81 pts Some context free languages are regular. Group of answer choices True...