![Problem 1 Create a CFG that generates each of the languages below. [10 points] [10 points] wR is a substring of r if there are strings y, z E {a, b) such that r = ywR2. A = {w I w E {a, b) has more as than bs} B = {w#r l w,xe(a, b) and wR a. b. is a substring of r). Rememb er, c. [10 points] C = {ambck 1 m, n > 0 and k = m + n).](http://img.homeworklib.com/questions/d3321a20-65fb-11eb-9508-dd66325f6b18.png?x-oss-process=image/resize,w_560)
Homework Answers
Below are the CFG's as per the languages specified by you:
Solution a.
S -> Ta | RS | SRT
T -> Ta | λ
R -> RR | aRb | bRa | λ
Solution b.
S → T R
T → aTa | bTb | #R
R → RR | a | b
Solution c.
S → aSc | B
B → bBc | λ
I hope I could solve your problem.Further, if you have any doubt, please ask.
Add Answer to:
Problem 1 Create a CFG that generates each of the languages below. [10 points] [10 points]...
Theory of Computation - Push Down Automata (PDA) and Context Free Grammars (CFG) Problem 1. From...
Theory of Computation - Push Down Automata (PDA) and Context
Free Grammars (CFG)
Problem 1. From a language description to a PDA Show state diagrams of PDAs for the following languages: a. The set of strings over the alphabet fa, b) with twice as many a's as b's. Hint: in class, we showed a PDA when the number of as is the same as the number of bs, based on the idea of a counter. + Can we use a...
Question 8 10 pts Let S = {a,b,c}. Write a grammar that generates the language: L...
Question 8 10 pts Let S = {a,b,c}. Write a grammar that generates the language: L = {(ac)"6n+1w: n > 0, W € 2*, W contains the substring acb}
Let L, be the language accepted by the DFA below and L2 = {0"1"Om1 mol 1|n,...
Let L, be the language accepted by the DFA below and L2 = {0"1"Om1 mol 1|n, m, k > 0}. Create a CFG that generates L3 = L, UL2 using the techniques pre sented in textbook. 0 start -> 0 10
Give a context free grammar for the language L where L = {a"bam I n>:O and...
Give a context free grammar for the language L where L = {a"bam I n>:O and there exists k>-o such that m=2"k+n) 3. Give a nondeterministic pushdown automata that recognizes the set of strings in L from question 3 above. Acceptance should be by accept state. 4. 5 Give a context-free grammar for the set (abc il j or j -k) ie, the set of strings of a's followed by b's followed by c's, such that there are either a...
1. Give a context-free grammar for the set BAL of balanced strings of delimiters of three...
1. Give a context-free grammar for the set BAL of balanced strings of delimiters of three types (), and . For example, (OOis in BAL but [) is not. Give a nondeterministic pushdown automata that recognizes the set of strings in BAL as defined in problem 1 above. Acceptance should be by accept state. 2. Give a context free grammar for the language L where L-(a"b'am I n>-o and there exists k>-o such that m-2*ktn) 3. Give a nondeterministic pushdown...
Problem 1. (10 points) For each of the following statements determine whether it is true or...
Problem 1. (10 points) For each of the following statements determine whether it is true or false. * (+1 for correct, 0 for blank, -0.5 for incorrect) The grammar SaSb generates {w € {a,b}" : #a = #b}. T F A CFG is ambiguous if there is exactly one parse tree for every word. TF Two different CFGs could generate two different languages. T F An NPDA could have no final states and still accept the word abba. T F...
disprove that the given lan 4. [20 Points For each of the following languages, prove or guage is regular (a) L1www e {a...
disprove that the given lan 4. [20 Points For each of the following languages, prove or guage is regular (a) L1www e {a,b}*} {w w E {a, b}* and no two b's in w have odd number of a's in between}. (b) L2 (c) L3 a" (d) L4 vw n = 3k, for k > 0}. a, b}*}
disprove that the given lan 4. [20 Points For each of the following languages, prove or guage is regular (a) L1www e...
Construct context-free grammars that generate each of these languages: A. tw E 10, 1 l w...
Construct context-free grammars that generate each of these languages: A. tw E 10, 1 l w contains at least three 1s B. Hw E 10, 1 the length of w is odd and the middle symbol is 0 C. f0, 1 L fx l x xR (x is not a palindrome) m n. F. w E ta, b)* w has twice as many b's as a s G. a b ch 1, J, k20, and 1 or i k
2. (10 points) Determine whether the following languages are decidable, recognizable, or undecidable. Briefly justify y...
2. (10 points) Determine whether the following languages are decidable, recognizable, or undecidable. Briefly justify your answer for each statement. 1) L! = {< D,w >. D is a DFA and w E L(D)} 2) L2- N, w> N is a NF A and w L(N) 3) L,-{< P, w >: P is a PDA and w ㅌ L(P); 4) L,-{< M, w >: M is a TM and w e L(M)} 5) L,-{< M, w >: M is a...
Question 3 Give a context-free grammar for each of the following languages over = {a,b,c}. 1....
Question 3 Give a context-free grammar for each of the following languages over = {a,b,c}. 1. {a^jen: n >0}. 2. {animck : k=n+m} 3. Strings of a's and b's that contain twice as many a's as b's (for example, aba).
Theory of Computation - Push Down Automata (PDA) and Context
Free Grammars (CFG)
Problem 1. From a language description to a PDA Show state diagrams of PDAs for the following languages: a. The set of strings over the alphabet fa, b) with twice as many a's as b's. Hint: in class, we showed a PDA when the number of as is the same as the number of bs, based on the idea of a counter. + Can we use a...
Question 8 10 pts Let S = {a,b,c}. Write a grammar that generates the language: L = {(ac)"6n+1w: n > 0, W € 2*, W contains the substring acb}
Let L, be the language accepted by the DFA below and L2 = {0"1"Om1 mol 1|n, m, k > 0}. Create a CFG that generates L3 = L, UL2 using the techniques pre sented in textbook. 0 start -> 0 10
Give a context free grammar for the language L where L = {a"bam I n>:O and there exists k>-o such that m=2"k+n) 3. Give a nondeterministic pushdown automata that recognizes the set of strings in L from question 3 above. Acceptance should be by accept state. 4. 5 Give a context-free grammar for the set (abc il j or j -k) ie, the set of strings of a's followed by b's followed by c's, such that there are either a...
1. Give a context-free grammar for the set BAL of balanced strings of delimiters of three types (), and . For example, (OOis in BAL but [) is not. Give a nondeterministic pushdown automata that recognizes the set of strings in BAL as defined in problem 1 above. Acceptance should be by accept state. 2. Give a context free grammar for the language L where L-(a"b'am I n>-o and there exists k>-o such that m-2*ktn) 3. Give a nondeterministic pushdown...
Problem 1. (10 points) For each of the following statements determine whether it is true or false. * (+1 for correct, 0 for blank, -0.5 for incorrect) The grammar SaSb generates {w € {a,b}" : #a = #b}. T F A CFG is ambiguous if there is exactly one parse tree for every word. TF Two different CFGs could generate two different languages. T F An NPDA could have no final states and still accept the word abba. T F...
disprove that the given lan 4. [20 Points For each of the following languages, prove or guage is regular (a) L1www e {a,b}*} {w w E {a, b}* and no two b's in w have odd number of a's in between}. (b) L2 (c) L3 a" (d) L4 vw n = 3k, for k > 0}. a, b}*}
disprove that the given lan 4. [20 Points For each of the following languages, prove or guage is regular (a) L1www e...
Construct context-free grammars that generate each of these languages: A. tw E 10, 1 l w contains at least three 1s B. Hw E 10, 1 the length of w is odd and the middle symbol is 0 C. f0, 1 L fx l x xR (x is not a palindrome) m n. F. w E ta, b)* w has twice as many b's as a s G. a b ch 1, J, k20, and 1 or i k
2. (10 points) Determine whether the following languages are decidable, recognizable, or undecidable. Briefly justify your answer for each statement. 1) L! = {< D,w >. D is a DFA and w E L(D)} 2) L2- N, w> N is a NF A and w L(N) 3) L,-{< P, w >: P is a PDA and w ㅌ L(P); 4) L,-{< M, w >: M is a TM and w e L(M)} 5) L,-{< M, w >: M is a...
Question 3 Give a context-free grammar for each of the following languages over = {a,b,c}. 1. {a^jen: n >0}. 2. {animck : k=n+m} 3. Strings of a's and b's that contain twice as many a's as b's (for example, aba).
Most questions answered within 3 hours.
-
The tires of a car make 61 revolutions as the car reduces its
speed uniformly from...
asked 3 minutes ago -
Peabody, Inc., sells fireworks. The company’s marketing director
developed the following cost of goods sold budget...
asked 7 minutes ago -
A signal transduction pathway includes the steps listed
below.
1. An inactive signal transduction molecule is...
asked 6 minutes ago -
1. The correlation coefficient determined for two variables has
a value of 0.89. Describe, in words,...
asked 12 minutes ago -
The following data relate to direct materials costs for
November:
Actual costs
4,700 pounds at $5.35...
asked 10 minutes ago -
Kyle, a 95.0 kg football player, leaps straight up into the air
(with no horizontal velocity)...
asked 34 minutes ago -
Which of the following is a measure of profitability?
A.
Quick (acid-test) ratio
B.
Net sales...
asked 37 minutes ago -
Find the total pressure exerted by 2 grams of ethane and 3 grams
of CO2 contained...
asked 38 minutes ago -
A fireman standing on a 5.2 m high ladder operates a water hose
with a round...
asked 34 minutes ago -
A cream formulation is studied for accelerated stability study.
Creaming was observed when formulation was tested...
asked 37 minutes ago -
A 1,150 lumen light bulb is placed 37 cm in front of a mirrored
wall, whose...
asked 48 minutes ago -
Given that z is a standard normal random variable, compute the
following probabilities (to 4 decimals)....
asked 54 minutes ago