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}

Give a push down automaton M that accepts the following language over E = {0,1}: L(M) = L={w: w contains at least three 0's and at most one 1}. Full credits are given only if your machine is a PDA and your *.jff passes all the tests.

22 Turing machine L = { a^ cb" | n>0} input Tap ·B |a|aa|cb|ob| Kala ы в в B|B X (Y, Y, R) (a,a, R) (C,C, R) (a,x, R) (Y, Y,R) Squ (C,C,R) 93 (b, Y,L), (B,B, 4R), (X, X, R) { replace a with x and b with Y. (a, a, L) (C,C,L) (X,Y, L) (Y,Y, R) (af)

Let L = { M| M is a Turing machine and L(M) is set of all binary 0,1-strings of even length}, where L(M) is the language accepted by Turing machine M.  Prove that L is undecidable by finding a reduction from  to it, where ={<M,w>| M is a Turing machine and M accepts w}.

Let Z = { 0 0 ! , 0 1 ! , 1 0 ! , 1 1 ! }. Decide whether each of the following languages over Σ is regular: • The set of all strings such that the “top row” is the reverse of the bottom “row.” For instance, 0 0 ! 1 0 ! 0 1 ! 0 0 ! ∈ L, and 0 0 ! 1 1 ! 0 1 ! 0 0 ! ∈/ L, • The set of all strings such that the “top row” is the complement of the bottom “row.”

Show that the language K = {(M) | M is a TM and does not accept (M)} is not Turing-recognizable. Note: Prove by contradiction. No need to do a reduction from another problem. Additionally, you must show every step of your proof clearly.

Exercise 2.29 Describe an algorithm that, given finite automata accepting lan- guages L1 and L2, determines if L1L2 = 0. %3D

L = { <A,B> | A and B are PDAs and L(A) L(B) } a) prove that L is undecidable b) Prove that L is not Turing recognizable

draw all 3 turing machine by hand

Computer Science Show that the language L is regular. show your work, i am trying to learn this.