Assumptions for this exercise ... • Grammar G = ({S, A, B}, {a,b}, S, {S → abS, S → A, A → baB, B → aA, To do in this exercise ... • Construct a Deterministic Finite Accepter M such that L(M) = L(G), the language generated by grammar G. • Save your Deterministic Finite Accepter as a JFLAP.jff file, and submit that .jff file to Canvas as your solution to this exercise.

Assumptions for this exercise ... • Grammar G = ({S, A, B}, {a,b}, S, {S → abS, S → A, A → baB, B → aA, To do in this exercise ... • Construct a Deterministic Finite Accepter M such that L(M) = L(G), the language generated by grammar G. • Save your Deterministic Finite Accepter as a JFLAP.jff file, and submit that .jff file to Canvas as your solution to this exercise.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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What can be claimed about the grammar G: {S→ alaRb, R→ b|bSa }? OA. G is a context-free grammar and L(G) is a context-free language. B. G is a context-free grammar but L(G) is actually a regular language. O C. G is a regular grammar and L(G) is a regular language. What can be said about the grammar G: {S → ORO|OR1|1RO|1R1, R → E|OR|1R }? OA. G is a context-free grammar and L(G) is a context-free language. B. G is a context-free grammar but L(G) is the regular language (0+1)²(0+1)* C. G is a regular grammar and L(G) is the regular language (0+1)(0+1)*
Answer the given question with a proper explanation and step-by-step solution. Using the algorithm discussed in class, ”Big loop algorithm” show the transition diagram for a pushdown automaton (PDA) to recognize the language generated by G, which ahs the following grammer rules S →BAC A →a | b | c | ε B →bB | b C →cC | ε Fully define for the grammar G above, that is G = (....Describe in English what language the grammar G generates . Give an example showing that the grammar G above is ambiguous
2. Prove that the language L(G) is not regular where G is the following cfg: G= ({S,A,B}, {a,b,c}, {S→Abbb|B, A→aS, B c}, S). Note: You must first determine L(G).
(I) State the pumping lemma with all its conditions and indicate how you go about proving that a language is not regular. (II) If the languages are regular, give an automaton. Otherwise, show it is not regular by using pumping lemma. L= {b²anbma³ | m, n ≥ 0}. L = {b²anbma³ | m = n}. L = {ww|w is any string over {a.b}} L = {a³b4} L= {anbn+1} L = {ambnamn | m,n≥ 0 }
(A) Design in JFLAP a simulator of a deterministic finite automaton (DFA) that (only) recognizesthe language Λ, where Λ is the first letter of your family name. (B) Test the simulator for one accepting and one rejecting string.Language ABinary numbersExample: A = {00000000, 0101, 111111,
Complete the proof of Theorem 6.4. Theorem 6.4: Let G = (V, T, S, P) be any context-free grammar without λ-productions. Then there exists a context-free grammar bG = (bV , b T, S, b P) that does not have any unit-productions and that is equivalent to G. 1
Assumptions ... • Alphabet Σ = {a, b} . L₁= {ab n ≥ 0 An mod 3=0} L₂= {am: n ≥0^m≥ 0^n=m-1} ● . To do in this exercise ... Find a context-free grammar G such that L(G) = L₁ U L2. • Save your context-free grammar as a JFLAP .jff file, and submit that .jff file to Canvas as your solution to this exercise.
3. For the following, prove context free by giving CFG or describe PDA. If not context free then prove it using Pumping Lemma: ak bi |k>(j-1)? wtwR | w.t in (alb)* and |t|=|w|. Hint: not CF b. wtwR w.t in (alb)*. (Hint: CF) а. с. For any grammar that you write, answer if ambiguous or not (or unknown). Explain.
Prove that the following language is regular.L = {x | x ∈ {0, 1}∗, x does not contain five consecutive 0's or five consecutive 1's}Hint: You may take advantage of some closure properties.
3. Prove context free (give CFG or describe PDA) or not (Pumping Lemma): ak bi |k>(j-1)2 b. wtwR | w,t in (a|b)*. (Hint: CF) а. wtwr | w,t in (alb)* and [t|=|w|. Hint: not CF с. For any grammar that you write, answer if ambiguous or not (or unknown). Explain.
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…
Given L ={ambn | m< n }. Derive (i) a context-free grammar that accepts L (ii) a PDA accepting L by empty store (iii) a PDA accepting L by final state.