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...
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 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}. (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...
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}* and w = wr}. So L is a palindrome made up of the letters a, b, c, d, and e.
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
Let L be the language {0n 1m : n ≤ m ≤ 2n}. Is L regular? contextfree but not regular? or not context-free? Show that your answer is correct.
I need to construct a deterministic finite automata, DFA M, such that language of M, L(M), is the set of all strings over the alphabet {a,b} in which every substring of length four has at least one b. Note: every substring with length less than four is in this language. For example, aba is in L(M) because there are no substrings of at least 4 so every substring of at least 4 contains at least one b. abaaab is in...