Homework Answers
1. L is the set of strings over {a, b) that begin with a and do...
1. L is the set of strings over {a, b) that begin with a and do not contain the substring bb. a. Show L is regular by giving a regular expression that denotes the language. b. Show L is regular by giving a DETERMINISTIC finite automaton that recognizes the language.
(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...
sigma = {a, b, c, d, e} Show that L = { w ∈ sigma* |...
sigma = {a, b, c, d, e} Show that L = { w ∈ sigma* | substring abcd occurs at most once in w} is an FSL.
Let ?= (a, b). The Language L = {w E ?. : na(w) < na(w)) is...
Let ?= (a, b). The Language L = {w E ?. : na(w) < na(w)) is not regular. (Note: na(w) and nu(w) are the number of a's and 's in tw, respectively.) To show this language is not regular, suppose you are given p. You now have complete choice of w. So choose wa+1, Of course you see how this satisfies the requirements of words in the language. Now, answer the following: (a) What is the largest value of lryl?...
3) Construct a regular expression defining each of the following languages over the alphabet {a, b}....
3) Construct a regular expression defining each of the following languages over the alphabet {a, b}. (a) L = {aab, ba, bb, baab}; (b) The language of all strings containing exactly two b's. (c) The language of all strings containing at least one a and at least one b. (d) The language of all strings that do not end with ba. (e) The language of all strings that do not containing the substring bb. (f) The language of all strings...
Give regular expressions for the following languages: (a) The language of all strings over {a,b} except...
Give regular expressions for the following languages: (a) The language of all strings over {a,b} except the empty string. (b) The language of all strings over {a,b} that contain both bab and bba as substrings. (c)L k = {w ∈ {a,b} * | w contains a substring having 3 more b’s than a’s}. (d) The language of all strings over {a,b} that have a b in every odd position (first symbol is considered position 1; empty string should be accepted)...
Find a regular expression for the following language over the alphabet Σ = {a,b}. L = {strings th...
Find a regular expression for the following language over the alphabet Σ = {a,b}. L = {strings that begin and end with a and contain bb}.
Prove that the following language is not regular: L = { w | w ∈ {a,b,c,d,e}*...
Prove that the following language is not regular: L = { w | w ∈ {a,b,c,d,e}* and w = wr}. So L is a palindrome made up of the letters a, b, c, d, and e.
Let L be the language of binary strings of odd length such that the middle bit...
Let L be the language of binary strings of odd length such that the middle bit is 0. Show that L is not regular, and show that L is context-free.
The grammartofsm algorithm: Let L be the language described by the following regular grammar: a. For...
The grammartofsm algorithm:
Let L be the language described by the following regular grammar: a. For each of the following strings, indicate whether it is a member of L: v. zyyzz b. Use grammartofsm (Rich 2008; page 157) to construct an FSM that accepts L c. Give a concise (but complete) description of L in plain English. We were unable to transcribe this image
1. L is the set of strings over {a, b) that begin with a and do not contain the substring bb. a. Show L is regular by giving a regular expression that denotes the language. b. Show L is regular by giving a DETERMINISTIC finite automaton that recognizes the language.
(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...
Let ?= (a, b). The Language L = {w E ?. : na(w) < na(w)) is not regular. (Note: na(w) and nu(w) are the number of a's and 's in tw, respectively.) To show this language is not regular, suppose you are given p. You now have complete choice of w. So choose wa+1, Of course you see how this satisfies the requirements of words in the language. Now, answer the following: (a) What is the largest value of lryl?...
The grammartofsm algorithm:
Let L be the language described by the following regular grammar: a. For each of the following strings, indicate whether it is a member of L: v. zyyzz b. Use grammartofsm (Rich 2008; page 157) to construct an FSM that accepts L c. Give a concise (but complete) description of L in plain English. We were unable to transcribe this image
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