1. For a string s e 0, î, 2;" and a symbol d e { 0,1,2} let #(s, d) denote the number of times d appears in s. For example, #(0120012, 0)-3. Consider the language: {0, 1, 2. #(11,0) L- #(w, 1), #...
For a string s ∈ {0, 1} let denote the number represented by in the binary * s2 s numeral system. For example 1110 in binary has a value of 14 . Consider the language: L = {u#w | u,w ∈ {0, 1} , u } , * 2 + 1 = w2 meaning it contains all strings u#w such that u + 1 = w holds true in the binary system. For example, 1010#1011 ∈ L and 0011#100 ∈...
1. Construct a DFSM to accept the language: L w E ab): w contains at least 3 as and no more than 3 bs) 2. Let E (acgt and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg. ge. Construct both a DFSM to accept the language and a regular expression that represents the language. 3. Let ab. For a string w E , let w denote the string w with the...
1. Construct a DFSM to accept the language: L = {w € {a,b}*: w contains at least 3 a's and no more than 3 b's} 2. Let acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, gc. Construct both a DFSM to accept the language and a regular expression that represents the language 3. Let a,b. For a string w E ', let W denote the string w with the...
DO NUMBER 3 2. Let {acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, gc. Construct both a DFSM to accept the language and a regular expression that represents the language 3. Let a,b. For a string w E X", let W denote the string w with the a's and b's flipped. For example, for w aabbab: w bbaaba wR babbaa abaabb {wwR Construct a PDA to accept the language:...
DO NUMBER 4 AND 5 2. Let {acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, gc. Construct both a DFSM to accept the language and a regular expression that represents the language 3. Let a,b. For a string w E X", let W denote the string w with the a's and b's flipped. For example, for w aabbab: w bbaaba wR babbaa abaabb {wwR Construct a PDA to accept...
Problem 3.3: For a string x € {0,1}*, let af denote the string obtained by changing all 0's to l's and all l's to O's in x. Given a language L over the alphabet {0,1}, define FLIP-SUBSTR(L) = {uvFw: Uvw E L, U, V, w € {0, 1}*}. Prove that if L is regular, then FLIP-SUBSTR(L) is regular. (For example, (1011)F = 0100. If 1011011 e L, then 1000111 = 10(110) F11 € FLIP-SUBSTR(L). For another example, FLIP-SUBSTR(0*1*) = 0*1*0*1*.)...
Given any string w ∈ {0, 1}∗, let n0(w) = number of 0′s in w and n1(w) = number of 1′s in w. Prove, by using the pumping lemma, that the language {w | 0 ≤ n0(w) ≤ 2∗n1(w)+1.} is not a regular language.
Question 1. Let S = {a,b}, and consider the language L = {w E E* : w contains at least one b and an even number of a's}. Draw a graph representing a DFA (not NFA) that accepts this language. Question 2. Let L be the language given below. L = {a”62m : n > 0} = {1, abb, aabbbb, aaabbbbbb, ...} Find production rules for a grammar that generates L.
E={a,b,c,d}, L = {anbmchdm : n, m 2 0}. For example, s = aabccd e L because the symbols are in Unicode order, and #a(s) = #c(s), #(s) #c(s), #b(s) = #a(s); ac e L for the same reason; s = abcdd & L because #b(s) #a(s); and acbd & L beause the symbols are not in Unicode order. Prove that L & CFLs using the CF pumping theorem, starting by defining w such we Land |w| 2 k. Remember...
2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3 times) a technician is called on an emergency call. The joint probability distribution fxy(x, y) is given by 1 0.05 0.05 0 0.05 0.1 0.2 0.1 0.35 0.1 (a) Evaluate the marginal pdf and the mean of X (b) Evaluate the marginal pdf and the mean of Y....