Prove that L = {ww|wɛ (a, b)*} is not context-free. Then, design a Turing Machine that аcсepts L.

Consider the language L = { |‡x such that ï ¤ L(M₁)~ L(M₂)}. Show that L is not decidable.

Consider the following language L over Σ = {0, 1, 2}:  L = { 0i2 1 2 02i1i | i ≥ 0 } 1. Construct a Turing machine accepting L. Justify your answer, explaining how the TM youconstructed will accept words in the language L. 2. Give an accepting run of your TM for the word 0212001 Hint: think about the TM accepting the language { 0i2 1 2 02i1i | i ≥ 0 } and how can it be changed to accept the language above. Notation: recall that e.g. we write 0i for the word consisting of i-many 0’s.

Please written by computer source Let x be a binary string. The minimal description of x, written d(x), is the shortest string ⟨M, w⟩ where TM M on input w halts with x on its tape. If several such strings exist, select the lexicographically first among them. The descriptive complexity, or Kolmogorov complexity, of x, written K(x), is K(x) = |d(x)|. Show that the function K(x) is not a computable function. HINTS: If K is a computable function, there is some TM which computes it. That TM can be used to find strings of large complexity. Try to design a program which outputs “complex” strings but which contradicts their supposed complexity, and even contradicting the supposed complexity of a single string suffices.

2. Let A be a Turing-recognizable language consisting of descriptions of Turing machines, i.e., A = {(M1), (M2),...}, where every M; is a decider. Prove that some decidable language D is not decided by any decider M, whose description appears in A.

Do fast plz

not handwritten   Prove that the following problem is not decidable: Given a Turing Machine M, does the machine reject every input. (i.e., does L(M) = ∅)?

Give the transition diagram of a standard Turing Machine that implements the function. Brie y explain your solution strategies.

LetΣ ={a, b}. LetL={aibai|i≥0}.Give a Turing machine (TM) that accepts the languageL.Assume (as in the examples done in our course videos) that, when theTM starts, the head is on a blank symbol,∆, and the input string isimmediately after that blank symbol on the tape. For example, if theinput string wereaaabaaa, then the inital tape configuration would be∆aaabaaa