Problem 8: Design a Turing machine that takes inputs like ...B1110111111B.... deletes the middle 0, and keeps the same number of 1s (so, in this case, it should output ...B111111111B...). This can be thought of as adding two numbers.
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- Example 9.7 For E = {a,b}, design a Turing machine that accepts L= {a,b„:n21}. Intuitively, we solve the problem in the following fashion. Starting at the leftmost a, we check it off by replacing it with some symbol, say x. We then let the read-write head travel right to find the leftmost b, which in turn is checked off by replacing it with another symbol, say y. After that, we go left again to the leftmost a, replace it with an x, then move to the leftmost band replace it with y, and so on. Traveling back and forth this way, we match each a with a corresponding b. If after some time no a's or b's remain, then the string must be in L. Working out the details, we arrive at a complete solution for which Q= {qo91;9293,94},F= {q4}, E= {a,b},T={a,b, x, y,¤}. The transitions can be broken into several parts. The setShow that the following function is Turing-computable. f(x)=x+1 . I want the drawingYou will disappoint me if you solve it without drawing I just want you to draw me the following question please: Turing machine that computes the function f(x,y) = x+2y, with both x and y strictly positive integers.
- 4. Draw the Turing machine that computes the function f(x,y) = x+2y, with both x and y strictly positive integers.Not so. The real question states that: Construct a turing machine that computes the function ?(?) = 2?, , i.e. if the input is 0^? then the output would be 0^2? e.g. if it says 000 on the tape before the machine is run it should read 000000 on the tape when it has stopped.Design a Turing machine M that decides the language L = {0n1n|n> 0}.
- b/a/L c/c/L a/c/R c/b/R a/c/R a/b/L c/a/L bp/R b/b/R a/a/R c/c/R (b) In this part we are looking at the Turing-Machine above. We assume here that b is the blank symbol, {a,c} is the input alphabet. (1) Give two words recognised by this Turing Machine. (ii) Give a computation for the input cc. If you think the computation diverges, give the first 5 configurations of the computation.4. 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∆aaabaaaBuild a Turing Machine T.M. with three tracks that receives two binary numbers and indicates which of the two is higher. We will consider that the data are stored in the first two tracks and aligned to the right, it means, the least significant bits of both are located in the same column. In the third track it will be written a B, a L or an E, indicating respectively that the first number is larger, smaller or equal to the second.
- A common problem that arises in software maintenance is identifying (and then removing) dead code, code that will never be executed no matter what input the program is given. The analogous problem for TMs would be to determine if a state is never entered, no matter what input the TM is given. Prove by reduction that Ldead, the set of pairs (T,s) where T is a Turing machine and s is a dead state, is not recursive.The puzzle called the Towers of Hanoi consists of three pegs, one of which contains several rings stacked in order of descending diameter from bottom to top. The problem is to move the stack of rings to another peg. You are allowed to move only one ring at a time, and at no time is a ring to be placed on top of a smaller one. Observe that if the puzzle involved only one ring, it would be extremely easy. Moreover, when faced with the problem of moving several rings, if you could move all but the largest ring to another peg, the largest ring could then be placed on the third peg, and then the problem would be to move the remaining rings on top of it. Using this observation, develop a recursive algorithm for solving the Towers of Hanoi puzzle for an arbitrary number of rings.Computer Science provide a three-tape turing machine for L = a^n where n => 0 is perfect square. λ should be accepted. tape 1: string to be processed n^2 a's tape 2: strings of length n^2. These sequences will be made up of symbol Y tape 3: strings of length n. These sequences should be made up of symbol Y. Tape 2 and 3 recursively generated from string 1, only last string retained on tape.