6. Let M = (Q,E, 8, qo, F') be the DFA given by the state diagram: 1 (a) Compute ô(qh, 110). (b) Determine whether 01 is accepted by M. (c) Compute L(M), the language accepted by M.
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Part A has to be in Delta HAT
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- 15. Prove that the language consisting of all the words in the alphabet {A, B, C} that start with C and have twice as many Bs as Cs and three times as many As than Bs is not context-free.Could you assist me with this issue? I'm struggling to comprehend the solution, and it would be helpful if you could offer a visual representation to clarify the question. Additionally, would you be able to walk me through the steps that lead to the answer, making sure to explicitly reference the Pigeonhole Principle in order to address this question? Can you please construct a NFA question that I need help with:1.60 Let Σ = {a, b}. For each k ≥ 1, let Ck be the language consisting of all strings that contain an a exactly k places from the right-hand end. Thus Ck = Σ∗ aΣ k−1 . Describe an NFA with k + 1 states that recognizes Ck in terms of both a state diagram and a formal description.Let Σ = {0, 1,#}. Show that the following language over Σ is not context-free: {x#y#z: x,y,z = {0,1}* and bin(x) + bin(y) = bin (z)}
- Provide DFA diagrams to recognizes the same languages as each of the regular expressions in a. The set of chess moves, in the formal notation, such as p-k4 or kbp x qn. b. All stings of a’s and b’s that do not contain the substring abb. c. All strings of a’s and b’s that do not contain the subsequence abb.For the language, draw the corresponding DPDA. L ={an b2n | N >0}, and Σ={a, b}.1. Give a CFL for the language L (over the alphabet {a, b}), where L = {w | w has exactly the same number of a's as b's.}2. Draw a nondeterministic PDA for the language from the previous question.
- 1) Given the following English descriptions of a language, write a regular expression that defines the language, and draw the state diagram of a DFA that accepts the language. For all languages, let Σ = {a, b}.a) The language consisting of all words having a number of a's that is a multiple of 3.b) The language consisting of all words that contain "babb".c) The language consisting of all words that end in "ba".d) The language consisting of all words that do not end in "ba".Draw the diagram of the NFA that recognizes the given language with the following regular expression (sigma)={ a , b }.Find a CFG that generates the language : L = {a i bj c jd i : i, j ≥ 1}
- Suppose the languages recognized by DFAs M and N are L1 and L2 respectively. How can we use DFAs M and N to construct a DFA that recognizes the language L1∩L2? [Can you use De Morgan's Law?]Describe a DFA that accepts each of the following languages. Describe briefly what each state in your DFA means. Do not attempt to draw your DFA, since the number of states could be huge; instead, give a mathematically precise description of the states Q, the start state s, the accepting states A, and the transition function δ All strings x ∈ {0, 1}* such that x contains 0^9 as a substring, or |x| is divisible by 8, or #0(x) − #1(x) is divisible by 7. #0(x) denotes the number of 0's in x, and #1(x) denotes the number of 1's in x.Let M be the PDA defined by Q = {q, q0 , q1 , q2}, Σ = {a,b}, Γ = {a}, F := {q , q1}.δ(q0 , a , Z0) = {(q, Z0 ) } δ(q , a, Z0) = {(q , aZ0)} δ(q , a, a) = {(q , aa)} δ(q , b , a) = {(q1 ,e)} δ(q1 , b , a) = {(q1 ,e)} δ(q1 , b, Z0 ) = {(q2 , e)} Describe the CFG and the language accepted by M