Final Answer:
(a) L5={ww: w E{a,b}*}
For this language, you'll want a Turing machine that duplicates the input, verifies if the first half matches the second half, and then accepts or rejects accordingly. It involves traversing the input while simultaneously writing it onto a different part of the tape. By comparing the original input to the copied version, you can check if they match.
(b) L6={wuwR:w,uE{a,b}*,1w|=|u1}
To design a Turing machine for this language, you need to check if the input can be split into three parts: w, u, and a palindrome of '1w' (where 'w' is the same as 'w' but reversed). The machine should move to the beginning of 'w', then to the end of 'w', mark the start of 'u', move to the beginning of 'u', and then check if '1w' is a palindrome by comparing it with its reverse.
Explanation:
(a) For language L5={ww: w E{a,b}*}, the Turing machine design involves reading the input and simultaneously making a copy of it. By using states to traverse both sides of the input, the machine needs to ensure that the first half matches the second half. If it successfully verifies this, it accepts the input; otherwise, it rejects.
(b) Regarding language L6={wuwR:w,uE{a,b}*,1w|=|u1}, the Turing machine design strategy revolves around breaking the input into three segments: 'w', 'u', and a palindrome formed by '1w'. The machine must position itself correctly to differentiate these segments, then check if '1w' is indeed a palindrome by comparing it with its reversed version. If the conditions are met, the machine accepts the input; otherwise, it rejects it.
These designs involve careful tape manipulation, state transitions, and comparisons to ensure that the Turing machine recognizes the specified languages accurately. Implementing these designs would require crafting the transition functions, defining states, and managing the tape movement based on the conditions outlined for each language.