A tape-saving Turing machine is similar to an ordinary (deterministic) one-tape Turing machine, but it can read and write on both sides of each tape square: front and back. In addition, it can move the head to the middle of nonblank portion of the tape. Specifically, if the first s squares of the tape are not blank, then the head can move to square ds/2e. At each step, the head of the tape-saving TM can move left (L), right (R), switch sides of the current square (S) or jump to the middle (J). (a) Please give a formal definition of the form of the transition function of tape-saving TM.
(b) Show that tape-saving TMs recognize the class of Turing-recognizable languages, that is, they have exactly the same power as ordinary TMs.

Write a modular program (no classes yet, just from what you learned last year), that allows two players to play a game of tic-tac-toe. use a two-dimensional char array with 3 rows and 3 columns as the game board. each element of the array should be initialized with an asterisk (*). the program should display the initial board configuration and then start a loop that does the following: allow player 1 to select a location on the board for an x by entering a row and column number. then redisplay the board with an x replacing the * in the chosen location. if there is no winner yet and the board is not yet full, allow player 2 to select a location on the board for an o by entering a row and column number. then redisplay the board with an o replacing the * in the chosen location. the loop should continue until a player has won or a tie has occurred, then display a message indicating who won, or reporting that a tie occurred. player 1 wins when there are three xs in a row, a column, or a diagonal on the game board. player 2 wins when there are three ox in a row, a column, or a diagonal on the game board. a tie occurs when all of the locations on the board are full, but there is no winner. input validation: only allow legal moves to be entered. the row must be 1, 2, or 3. the column must be 1, 2 3. the (row, column) position entered must currently be empty (i.e., still have an asterisk in it).

What multimedia system creates an immersive, real-life experience that the user can interact with?

The output voltage of a power supply is assumed to be normally distributed. sixteen observations are taken at random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 9.25, 9.38, and 10.85