Consider the following language: {z€ {a, b}* | #a(x) 2#(x)} (a) Give a CFG for this set. (b) Prove that the given CFG is correct.
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- Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) DetermineFso that the product DFA recognizes: (i)L1∪L2(ii)L1∩L2(iii)L1\L2Based on your choice for F, for each case, provide a detailed proof why the product DFA recognizes each of the mentioned languages. Conclude that in-tersection of two regular languages is a regular language and set-theoretic dif-ference of two regular languages is regular.Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2. Using these two DFAs, can we construct a new DFA to recognize L1? If yes, construct it.If no, explain why.dont post any existing answers directly dislike Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2. Using these two DFAs, can we construct a new DFA to recognize L1? If yes, construct it.If no, explain why. Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2. Using these two DFAs, can we construct a new DFA to recognize…
- Please prove or disprove: If a language L ⊆ Σ∗ is recognized by a FA, then there is an NFA M = (K,Σ,δ,s0,F) with |F|= 1 such that L = L(M).Dont copy the answer otherwise will surely dislike Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2. Using these two DFAs, can we construct a new DFA to recognize L1? If yes, construct it.If no, explain why. Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2. Using these two DFAs, can we construct a new DFA to…Computer Science 5. Consider a language L over the binary alphabet. For any two binary strings x, y we say x, y are distinguishable by L if there exists a string w ∈ L such that exactly one of the strings xw, yw is in L. x, y are indistinguishable by L otherwise (denoted by idL. Prove that idL is an equivalence relation.
- Consider the following languages over the alphabet Σ = {a, b}: 1. L1 = {xwx : x, w ∈ Σ∗}2. L2 = {xwx : x, w ∈ Σ∗, |w| = 1}3. L3 = {xwx : x, w ∈ Σ∗, |x| = 1} For each language, decide whether it is regular or not regular. Prove each of your claims. If you construct a FA or a regular expression, you do not need to prove the correctness of your construction.If a language L ⊆ Σ∗ is recognized by a FA, then there is an NFA M = (K,Σ,δ,s0,F) with |F|= 1 such that L = L(M).Consider the languages L and L: L = {ww | w ∈ {a,b}∗}, all even-length strings of as and bs whose first and second halves are equal, and its complement L = {w | w ∈ {a,b}∗ ∧ w 6∈ L}, all strings of as and bs that are not in L. One of these languages is a CFL and the other is not. Either show that L or L̅ is context free by giving (design and formalize) either a PDA that recognizes it, or a CFG that generates it. Explain precisely why your PDA or CFG generates exactly L or L̅ .
- I added my incorrect answer and i think I am very close.I'm consistently arriving at an incorrect answer. Would you mind aiding me with question 2.7, specifically part C? I'm encountering challenges with this particular problem and would sincerely appreciate assistance in developing a state diagram for the push-down automaton in part C.question for 2.7 2.7 Give informal English descriptions of PDAs for the language. c. {w#x | w R is a substring of x for w, x ∈ {0,1} ∗ }For each of the following languages L, state whether L is regular, context-free but not regular, or not context-free and prove your answer. {xyx^R where x,y∈Σ^*} {xx^R yy^R{ where x,y∈Σ^*} {xx^R x{ where x∈Σ^*}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)}