I´ve been reading the paper "SOKOBAN and other motion planning problems" by Dorit Dor and Uri Zwick.
This is a link to the paper: Sokoban+ is pspace complete
In the paper, they proved that a problem called sokoban+ is pspace complete, they did it by reducing simulation of a turing machine with bounded tape to that problem.
sokoban+ is like sokoban, but the player can pull and push obstacles and all pieces are 2 x 1 rectangles (instead of 1 x 1 like in normal sokoban).
In figure 7, they show a drawing of the cell gadget, this represents a cell of a turing machine.
In the cell, the player enters, chosses a simbol (0 or 1) and if the player chooses correctly, he can go to a simbol gadgdet which will be open only if he has chosen the correct symbol. He goes through the symbol gadget, closing it, and then he goes to a gadget that forces the player to go to the next cell.
My question is, if in this cell and state the symbol of the tape has to change, how does the cell gadget registers that the symbol has changed?
Thanks for your help!