Question $($Design a Turing machine to solve the following problem: It should be checked whether a sequence of digits consisting of the digits $0,1,$ and $2$ is sorted in ascending order or not. For sequences such as $012,0001111122,222,$ or $000022,$ the symbol $\text{'}$s$\text{'}$ should be appended for "sorted". For sequences such as $21$ or $0011212,$ the symbol $\text{'}$U$\text{'}$ should be appended for "unsorted". Provide the set of states Z$,$ the initial state, the input alphabet L$,$ the tape alphabet $,$ and the transition table. Initially, the read$-$write head should be positioned before the first symbol, and at the end, it should be on the symbol S or U$.$ Comment on the meaning of each state or transition.$)$Answer: To design a Turing machine that checks whether a sequence of digits $(0,1,$ and $2)$ is sorted in ascending order or not, let's break down the components required:States $($Z$)$:$*$ q$0$: Initial state$*$ q$1$: Scan $0$s$*$ q$2$: Scan $1$s$*$ q$3$: Scan $2$s$*$ q$4$: Move left to check last element$*$ q$5$: Final state for "sorted"$*$ q$6$: Final state for "unsorted"Initial state: q$0$Input alphabet $($L$)$: $\{0,1,2\}$Tape alphabet: $\{0,1,2,$ s$,$ U$,$ #$,\}($where $\text{'}\text{'}$ represents blank symbol$)$Transition Table:$|$ State $|$ Symbol $|$ Next State $|$ Write $|$ Move $||-------|--------|------------|-------|-------||$ q$0|0|$ q$1|\_|$ R $||$ q$0|1|$ q$2|\_|$ R $||$ q$0|2|$ q$3|\_|$ R $||$ q$0|$ # $|$ q$5|$ s $|-||$ q$0|\_|$ q$6|$ U $|-||$ q$1|0|$ q$1|0|$ R $||$ q$1|1|$ q$2|1|$ R $||$ q$1|2|$ q$3|2|$ R $||$ q$1|$ # $|$ q$4|0|$ L $||$ q$2|0|$ q$6|$ U $|-||$ q$2|1|$ q$2|1|$ R $||$ q$2|2|$ q$3|2|$ R $||$ q$2|$ # $|$ q$4|1|$ L $||$ q$3|0|$ q$6|$ U $|-||$ q$3|1|$ q$6|$ U $|-||$ q$3|2|$ q$3|2|$ R $||$ q$3|$ # $|$ q$4|2|$ L $||$ q$4|0|$ q$6|$ U $|-||$ q$4|1|$ q$6|$ U $|-||$ q$4|2|$ q$6|$ U $|-||$ q$4|$ # $|$ q$0|$ # $|$ R $|$Commentary on transitions:$1.$ The machine starts in q$0$ and scans through the input, moving right$\mathrm{.}2.$ It encounters $0$s in q$1,1$s in q$2,$ and $2$s in q$3,$ moving right and rewriting respective symbols$\mathrm{.}3.$ If it reaches the end of the input marked by $\text{'}$#$\text{'}$ in q$0,$ it transitions to q$5$ and writes $\text{'}$s$\text{'}$ for sorted$\mathrm{.}4.$ If it encounters any inconsistencies while scanning $($e$.$g$.,$ a larger number following a smaller one$),$ it transitions to q$6$ and writes $\text{'}$U$\text{'}$ for unsorted$\mathrm{.}5.$ q$4$ is used to move left to the start of the input to verify the last element again$\mathrm{.}6.$ If the input is properly sorted until the end, it transitions to the respective final states q$5$ or q$6,$ appending $\text{'}$s$\text{'}$ or $\text{'}$U$\text{'}$ accordingly$\mathrm{.}7.$ The machine halts in either a sorted or unsorted state after marking the tape with $\text{'}$s$\text{'}$ or 'UIs this $100$ correct because I want sigma also to be used the expert used ai generarqted answer