
2. Give the first five strings in L-ordering for each of the following languages over 2...
Give the size of each of the following languages over S = {0, 1} below. If the language has no enough strings, then list all its strings. Let L1 = {ε, 1, 10}, L2 = {0, 01}, and LÆ = {}. a) |L1 – L2| = ____________ b) |L2L1 | = ___________ c) |L12|= __________ d) |L2LÆ| = ____________ e) |LÆ*|= ___________
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)...
For each of the following statements, where L1, L2, and L are languages over some alphabet Σ, state whether it is true or false. Prove your answer. • ∀L,(∅ or L+) = L∗ • ∀L1,L2,(L1 or L2)∗ = (L2 or L1)∗
(9) For each of the following languages L, give a simple English description. Show two strings that are in L and two that are not (unless there are fewer than two strings in L or two not in L, in which case show as many as possible). • L = {ω ∈ {a,b}∗| exactly one prefix of ω ends in a }. • L = {ω ∈ {a,b}∗| all prefixes of ω end in a }. • L = {ω...
Automata Question. Over the alphabet Σ = {0, 1}: 1) Give a DFA, M1, that accepts a Language L1 = {all strings that contain 00} 2) Give a DFA, M2, that accepts a Language L2 = {all strings that end with 01} 3) Give acceptor for L1 intersection L2 4) Give acceptor for L1 - L2
Part B - Automata Construction Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of all strings such that the number of 0s is divisible by 2 and the number of 1s is divisible by 5. Your DFA must handle all intput strings in {0,1}*. Here is a methodical way to do this: Figure out all the final states and label each with the shortest string it accepts, work backwards from these states to...
1. Give a DFA for each of the following languages defined over the alphabet Σ (0, i): a) (3 points) L={ w | w contains the substring 101 } b) (3 points) L-wl w ends in 001)
For each of the following statements. state whether it is True or False. Prove your answer: a. ∀L1 , L2(L1= L2)iff L1*·=L2*). b. (ØuØ*)n(¬Ø- (ØØ*)) = Ø (where ¬Ø is the complement of Ø). c. Every infinite language is the complement of a finite language. d. ∀L ((LR)R = L). e. ∀L1, L2((L1L2)*= L1*L2*). f. ∀L1, L2(( ((L1*L2*L1*)*= (L2UL1)*). g . ∀L1, L2(( ( ( L 1 U L 2 ) * = L 1 * U L 2 *...
(a) Give 2 strings that are members of language specified by the regular expression (0+ 1)∗ but are not members of the language specified by 0∗ + 1∗ . Then give 2 strings that are members of both languages. Assume the alphabet is Σ = {0, 1}. (b) For each of the following languages specified by regular expressions, give 2 strings that are members and 2 strings that are not members (a total of 4 strings for each part). Assume...
3. These languages are not regular. For each, list three strings that would work in a Pumping Lemma proof. Then, use one of them to show the language is not regular. But not a. a. L = {ww | w Î {a, b}*} b. L = {anba2n | n >= 0} c. {w Î S* | w contains more a’s than b’s}.