Prove that the following language is not regular: { w1aw2 | w1,w2 ∈ {a,b}* and |w1| = |w2| } In other words, L consists of strings of odd length over the alphabet {a, b} which have a as its middle symbol. SHOW ALL WORK, THANKS!
Prove that the following language is not regular: { w1aw2 | w1,w2 ∈ {a,b}* and |w1|...
1(a)Draw the state diagram for a DFA for accepting the following language over alphabet {0,1}: {w | the length of w is at least 2 and has the same symbol in its 2nd and last positions} (b)Draw the state diagram for an NFA for accepting the following language over alphabet {0,1} (Use as few states as possible): {w | w is of the form 1*(01 ∪ 10*)*} (c)If A is a language with alphabet Σ, the complement of A is...
Question 1 - Regular Expressions Find regular expressions that define the following languages: 1. All even-length strings over the alphabet {a,b}. 2. All strings over the alphabet {a,b} with odd numbers of a's. 3. All strings over the alphabet {a,b} with even numbers of b’s. 4. All strings over the alphabet {a,b} that start and end with different symbols. 5. All strings over the alphabet {a, b} that do not contain the substring aab and end with bb.
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}.
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...
Write the definition of a regular language. Use this or some other equivalent condition to prove that the set of strings (words) that define Integer numbers, like 33, 0, or -215 (but not -0), is a regular language.
Prove that the following language is regular or explain why it is nonregular: L = {amb" (m is odd and n is even) OR (m is even and n is odd))
Write down the regular expressions for the following set of strings over {a, b}: 1.Strings that contain no more than one occurrence of the string aa. 2.All strings containing aba: 3.All strings of odd length 4.A string in this language must have at least two a's. 5.All strings that begin with a, and have an even number of b Bonus - All strings with “a” at every odd position
John Doe claims that the language L, of all strings over the alphabet Σ = { a, b } that contain an even number of occurrences of the letter ‘a’, is not a regular language. He offers the following “pumping lemma proof”. Explain what is wrong with the “proof” given below. “Pumping Lemma Proof” We assume that L is regular. Then, according to the pumping lemma, every long string in L (of length m or more) must be “pumpable”. We...
Additional 9-13 Prove that the language {w#w|w is a string over the alphabet {a,b,c}} is not regular Tip: here are some strings in that language: abbc#abbc a#a aaa#aaa aaab#aaab cab#cab
1. (10 marks) Prove that the following languages are non-regular, using the Pumping Lemma. (a) (10 marks) L1 = {W € {0,1}* ||w| is odd, and the symbol in the very middle of the string is 0} For example, the strings 01011, 000000000 and 0 are in L1.]