(14 points) Given two languages L1=(a+b)*a and L2=b(a+b)*. Find a. L1 union L2 b. L1L2 (concatenation of L1 and L2 ) for a specially for part a I want you to show me the finite automata or FA in the work.
Added by Corey W.
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We will also provide finite automata (FA) for \( L_1 \) and \( L_2 \) as part of the solution. Show more…
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Consider the Deterministic Finite Automata, A = (QA, ΣA, δA, q0A, FA) and B = (QB, ΣB, δB, q0B, FB) with QA ∩ QB = ∅, ΣA ∩ ΣB = ∅ where ∅ stands for the null set. Let LA ⊆ ΣA* and LB ⊆ ΣB* be the languages accepted by A and B respectively and define the interleaved language: LA || LB := {s ∈ (ΣA ∪ ΣB)* | s ↑ A ∈ LA and s ↑ B ∈ LB} where s ↑ A and s ↑ B stand for the projection of s on ΣA and ΣB obtained by erasing all the symbols of s in ΣB and ΣA respectively. (a) Define the interleaving product A || B of A and B as a DFA that accepts the language LA || LB (b) Compute a DFA that accepts the language L = (0.1)* || (a.b)*
Sri K.
1. (10 points) DFA's: Design an DFA that recognizes the language L1 with the alphabet {0,1} (Draw the state diagram). L1 = {w ∈ {0, 1}* | w contains 11 as a substring} 2. (10 points) DFA's: Design an DFA that recognizes the language L2 with the alphabet {2,3} (Draw the state diagram). L2 = {w ∈ {2, 3}* | w ends with substring 23} 3. (10 points) NFA's: Design an NFA that recognizes the language L3 = L1 ∪ L2 with the alphabet {0, 1, 2, 3} (Draw the state diagram). 4. (10 points) Regular Expressions: Give a regular expression for L3. 5. (10 points) Design a Context-free grammar for L3 (specify the 4-tuple and all of the rules. Need not be in Chomsky normal form)
Let Σ = {a, b} L1 = {a, ab, abb} L2 = {λ, b, bb} Describe all the following languages as a set of strings. (i) L3 = L1 ∩ L2 (ii) L1L3 (iii) L3L1 (iv) L1L2
Madhur L.
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