Create a Turing machine that computes a mapping reduction from L1 ≤ m L2 where L1 ＝ {w : w ∈ {a,b}* and |W| is even} and where L2 ＝ {anbn : n ≥ 0}

Construct a finite state automaton which recognizes strings over {a, b} which begin withbaab or ends with babb.

NFA 0’s near end or 1 at end: Write a nondeterministic finite automaton with at most 10 states that decides whether its input is contained in the following set: {x ∈ {0, 1}∗ | x[|x| − 5] = x[|x| − 2] = 0 or x[|x|] = 1}. We index strings starting at 1, so x[1] is the first symbol, and x[|x|] is the last symbol.

Draw out a determinism Turing machine that computes a mapping reduction from L1 ≤ m L2 where L1 ＝ {w:w ∈ {a,b}* and |W| is even} and where L2 ＝ {anbn:n ≥ 0}.

For a Turing machine M, (M) refers to the binary representation of M. For a Turing machine M, L(M) contains the set of all strings accepted by M. For a Turing machine M and an input x = {0,1}*, Steps(M, x) refers to the number of steps taken by M to execute on x before it halts. Here, one step of execution of M on x = one movement (left or right) of the tape head. For a Turing machine M and an input x = {0,1}*, we define the following: ReachCells(M,x) = {i : M reaches ith tape cell when M is executed on x} Informally, it contains all locations on the tape that are visited when M is ecuted on x. The leftmost location on the tape is the first tape cell, the location next to it is the second tape cell, and so on. A string w₁ is an anagram of w2 if w₁ can be obtained by rearranging the alphabets of w2. Formally, if w₁ is an n length string, wê is called an anagram of w₁ if there exists a permutation à on n elements such that π(w₁) = W2.

The reverse function maps a string w to wR. Draw a multi-tape Turing machine that computes the reverse of a binary string. That is, given a binary string w as input, your Turing machine should compute wR, write the result to tape 1, and halt.

draw a Turing Machine that accepts strings in each of the languages below. Includethe septuple of the language with transition functions as well. a . L = { a n bn an bn : n  ≥ 1 } b . L = { a n b m an+m: n  ≥ 0, m ≥ 1} c . L = {w : w ∈ { a ,b}+ , |w| is a multiple of 4} d. L = {a n bm  bn  am  : m  ≥ 1 , n > m  } e. L = {wcw : w ∈ { a ,b}* }

Consider the language L = {w010w | w ∈ Ld} Is this language recursively enumerable? Justify your answer

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