If P = aabaab and = {a, b}, give a deterministic finite automaton for L(P), that is, the language of all strings which contain P as a substring.
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- Construct a finite automaton on the alphabet {s, t, u} that recognizes the language M, M = {x | such that x begins with st}Give a Finite Automaton of the language, over alphabet {a, b}, of strings that end with b.If the languages are regular, give an automaton. Otherwise, show it is notregular by using pumping lemma. L = {b2anbma3 | m = n}.
- Write a finite automaton for a language that accepts all words starting with an alphabet character that is not {for, while, if, int}, words can contain alphanumeric characters?Construct a finite state automaton which recognizes strings over {a, b} which begin withbaab or ends with babb.If the languages are regular, give an automaton. Otherwise, show it is notregular by using pumping lemma. L = {b2anbma3 | m = n}. Note: this is not the same question as L = {b2anbma3 | m, n ≥ 0}. If the solutions are the same please clearify.
- Let Σ be the alphabet {a,b}. Let L be the language describe by Σ∗ − (ε|Σ∗b)aa(ε|bΣ∗), where the hyphen denotes set difference and ε de- notes the empty string. (Hint: L consists of the strings over Σ in which no maximal substring consisting solely of a’s is of length 2.) Draw a finite automa- ton that accepts L.Draw a deterministic finite automaton (DFA) for the set of strings over the alphabet {a, b} whereeach string begins and ends with the same letter. For example, ababba and bbbab are strings thatshould be accepted by the DFA, but abbab and baaba should not be accepted.Use a closure operation to reduce the language L of all even-lengthed strings of as and bs where both halves of the string end with an a, that is L = {w0aw1a | w0,w1 ∈ {a,b}∗ ∧ |w0| = |w1|}, to a simpler language L0 which must also be regular if L is regular. Use the pumping lemma to show L0 is not regular.
- For the following regular language pairs; find Regular expressions and Finite Automata that define L1 ∩ L2. (WITH STEP BY PASS METHOD) L1 L2 All strings of even length a(a+b)* Even-Length strings (a+b)*aa(a+b)* Even-Length strings (b+ab)*(a+Λ) Odd-Length strings a(a+b)*Let L be the set of exactly those strings over the alphabet {a, b, c, g} whose last symbol is either a or g. Language L is accepted by a (noneterministic) finite automaton M = (Q, E, 5, q, F), where: E = {a, b, c, g}, Q= {q, s}, F= {s} and it is your task to complete the transition function 5 (given below) by filling all the editable empty spaces. q, a, [qs11] q, b, [q14] q, c, [q13] q g, [qs12] q, \lambda, [noneq]Write a deterministic automaton to recognize the language over {a, b, c}* such that every string of a’s must be followed by at least two c’s and every string of c’s must be followed by at least three b’s. {accepted strings: accbbb , aaacccbbbcbbb }