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)∗
For each of the following statements, where L1, L2, and L are languages over some alphabet...
If L1 and L2 are Regular Languages, then L1 ∪ L2 is a CFL. Group of answer choices True False Flag this Question Question 61 pts If L1 and L2 are CFLs, then L1 ∩ L2 and L1 ∪ L2 are CFLs. Group of answer choices True False Flag this Question Question 71 pts The regular expression ((ac*)a*)* = ((aa*)c*)*. Group of answer choices True False Flag this Question Question 81 pts Some context free languages are regular. Group of answer choices True...
1. (a) Give state diagrams of DFA’s recognizing the following languages. That alphabet is Σ = {a,b} L1 = {w | w any string that does not contain the substring aab} L2 = {w | w ∈ A where A = Σ*− {a, aa, b}} 2. (a) Give state diagrams of DFA’s recognizing the following languages. The alphabet is {0, 1}. L3 = {w | w begins with 0 ends with 1} (b) Write the formal definition of the DFA...
Suppose L1, L2, and L3 are languages and T1, T2, and T3 are Turing machines such that L(T1) = L1, L(T2) = L2, L(T3) = L3, knowing that T3 is recursive (always halts, either halts and accepts or halts and rejects) and both T1 and T2 are recursive enumerable so they may get stuck in an infinite loop for words they don't accept.. For each of the following languages, describe the Turing machine that would accept it, and state whether...
Let L1 = {ω|ω begins with a 1 and ends with a 0}, L2 = {ω|ω has length at least 3 and its third symbol is a 0}, and L3 = {ω| every odd position of ω is a 1} where L1, L2, and L3 are all languages over the alphabet {0, 1}. Draw finite automata (may be NFA) for L1, L2, and L3 and for each of the following (note: L means complement of L): Let L w begins...
2. If L1 and L2 are regular languages, which of the following are regular languages? Provide justification for your answers. a. L1 U L2 b. L1L2 c. L1 n L2
For each of the following claims, state whether it is True or False. Briefly explain your answer. (1) If Li and L2 are regular languages, then L1 L2 = {w:we (L1-L2) or w € (L2-L1)} is regular. (2) If Li and L2 are regular languages and L1 CL CL2, then L must be regular. (3) If Lis regular, then so is {xy : X E L andy & L}. (4) The union of a finite number of regular languages must...
Consider the following languages over the binary alphabet {a, b}: L:={a^nb^m:n≥m} Answer if it is regular or not, and prove it, and explain.
a.) Exhibit an algorithm that, given any three regular languages, L,L1,L2, determines whether or not L = L1L2. b.) Describe an algorithm by which one can decide whether two regular expressions are equivalent.
(10 pts.) Now assume that L and L2 are NP-complete languages. Which of the following statements are true? LiU L2 is NP-complete. Lin L2 is NP-complete. Li\L2 is NP-complete. (10 pts.) Now assume that L and L2 are NP-complete languages. Which of the following statements are true? LiU L2 is NP-complete. Lin L2 is NP-complete. Li\L2 is NP-complete.
The languages L1 = {anbm | m = n or m = 2n } and L2 = {a n b m | n <= m <= 2n } are context free. a. Choose one of the languages and write a CFG for it. b. Write the PDA that comes from your grammar (part a). Show the first 4 moves it would make on some string in your language (of length at least 4). Be sure to show state, input, and...