Clarity and precision (explanation)
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Clarity and precision (explanation)
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1. [5 Points) Let L be any non-empty language over an...
Let L be any non-empty language over an alphabet Σ. Show that L^2 ⊆ L^3 if...
Let L be any non-empty language over an alphabet Σ. Show that L^2 ⊆ L^3 if and only if λ ∈ L
(d) Let L be any regular language. Use the Pumping Lemma to show that In >...
(d) Let L be any regular language. Use the Pumping Lemma to show that In > 1 such that for all w E L such that|> n, there is another string ve L such that lvl <n. (4 marks) (e) Let L be a regular language over {0,1}. Show how we can use the previous result to show that in order to determine whether or not L is empty, we need only test at most 2" – 1 strings. (2...
4.[10 points] Let A be the language over the alphabet E-(a, b} defined by regular expression...
4.[10 points] Let A be the language over the alphabet E-(a, b} defined by regular expression (ab U b)*a U b. Give an NFA that recognizes A. Draw an NFA for A here.
4.[10 points] Let A be the language over the alphabet E-(a, b} defined by regular expression (ab U b)*a U b. Give an NFA that recognizes A. Draw an NFA for A here.
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe L using words. (c) (8pt...
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe L using words. (c) (8pt) Draw an automaton accepting L (ideally, deterministic).
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe...
1. (a) Let d be a metric on a non-empty set X. Prove that each of...
1. (a) Let d be a metric on a non-empty set X. Prove that each of the following are metrics on X: a a + i. d(1)(, y) = kd(x, y), where k >0; [3] ii. dr,y) d(2) (1, y) = [10] 1+ d(,y) The proof of the triangle inequality for d(2) boils down to showing b + > 1fc 1+a 1+b 1+c for all a, b, c > 0 with a +b > c. Proceed as follows to prove...
Can you please thoroughly explain part B? Let Σ {0,1} be an alphabet. Suppose the language...
Can you please thoroughly explain part B?
Let Σ {0,1} be an alphabet. Suppose the language Ly is the set of all strings that start with a 1 and L2 is the set of all strings that end in a 1. Describe Lj U L2 and (L1 UL2)* using English. b) Decide if the given strings belong to the language defined by the given regular expression. If it does not belong, then explain why. 0(1|€)10(e|0)*11 , strings: 0110011, 0100011001111
Consider the language defined over the alphabet Σ (0, 1): [10] 2nin i. Show that L1...
Consider the language defined over the alphabet Σ (0, 1): [10] 2nin i. Show that L1 is context-free by specifying a CFG Gi for L1 ii. Convert the CFG Gi to a pushdown automaton Pv that accepts L1 by empty 12 stack iii. Give a pushdown automaton PF that accepts L by final state
6. [5 points] Let Lo be the language over { = {0,1} consisting of strings having...
6. [5 points] Let Lo be the language over { = {0,1} consisting of strings having twice as many O's as it has l’s. For example, Lo contains the strings 001, 001010, 010100100. Use the Pumping Lemma to show that Lo is not regular. wice as many o's as it has I's
Please show all work so I can gain a better understanding. Thank you! (Let X ⊂ R n be non-empty a...
Please show all work so I can gain a better understanding. Thank
you!
(Let X ⊂ R n be non-empty and let A be an n×n matrix. Show that
A[co (X)] = co (A[X]). Here co means convex hull.)
Exercise 17: Let X C Rn be non-empty and let A be an n × n matrix. Show that Alco (X)-co (A Here co means convex hull. )
Exercise 17: Let X C Rn be non-empty and let A be an...
5. Let S be a non empty bounded subset of R. If a > 0, show...
5. Let S be a non empty bounded subset of R. If a > 0, show that sup (as) = a sup S where as = {as : ES}. Let c = sup S, show ac = sup (aS). This is done by showing (a) ac is an upper bound of aS. (b) If y is another upper bound of as then ac S7 Both are done using definitions and the fact that c=sup S.
(d) Let L be any regular language. Use the Pumping Lemma to show that In > 1 such that for all w E L such that|> n, there is another string ve L such that lvl <n. (4 marks) (e) Let L be a regular language over {0,1}. Show how we can use the previous result to show that in order to determine whether or not L is empty, we need only test at most 2" – 1 strings. (2...
4.[10 points] Let A be the language over the alphabet E-(a, b} defined by regular expression (ab U b)*a U b. Give an NFA that recognizes A. Draw an NFA for A here.
4.[10 points] Let A be the language over the alphabet E-(a, b} defined by regular expression (ab U b)*a U b. Give an NFA that recognizes A. Draw an NFA for A here.
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe L using words. (c) (8pt) Draw an automaton accepting L (ideally, deterministic).
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe...
1. (a) Let d be a metric on a non-empty set X. Prove that each of the following are metrics on X: a a + i. d(1)(, y) = kd(x, y), where k >0; [3] ii. dr,y) d(2) (1, y) = [10] 1+ d(,y) The proof of the triangle inequality for d(2) boils down to showing b + > 1fc 1+a 1+b 1+c for all a, b, c > 0 with a +b > c. Proceed as follows to prove...
Can you please thoroughly explain part B?
Let Σ {0,1} be an alphabet. Suppose the language Ly is the set of all strings that start with a 1 and L2 is the set of all strings that end in a 1. Describe Lj U L2 and (L1 UL2)* using English. b) Decide if the given strings belong to the language defined by the given regular expression. If it does not belong, then explain why. 0(1|€)10(e|0)*11 , strings: 0110011, 0100011001111
Consider the language defined over the alphabet Σ (0, 1): [10] 2nin i. Show that L1 is context-free by specifying a CFG Gi for L1 ii. Convert the CFG Gi to a pushdown automaton Pv that accepts L1 by empty 12 stack iii. Give a pushdown automaton PF that accepts L by final state
6. [5 points] Let Lo be the language over { = {0,1} consisting of strings having twice as many O's as it has l’s. For example, Lo contains the strings 001, 001010, 010100100. Use the Pumping Lemma to show that Lo is not regular. wice as many o's as it has I's
Please show all work so I can gain a better understanding. Thank
you!
(Let X ⊂ R n be non-empty and let A be an n×n matrix. Show that
A[co (X)] = co (A[X]). Here co means convex hull.)
Exercise 17: Let X C Rn be non-empty and let A be an n × n matrix. Show that Alco (X)-co (A Here co means convex hull. )
Exercise 17: Let X C Rn be non-empty and let A be an...
5. Let S be a non empty bounded subset of R. If a > 0, show that sup (as) = a sup S where as = {as : ES}. Let c = sup S, show ac = sup (aS). This is done by showing (a) ac is an upper bound of aS. (b) If y is another upper bound of as then ac S7 Both are done using definitions and the fact that c=sup S.
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