Halting game to Linear Chess we introduce a few concepts. Alternatively, show it requires exponential time. Grade A for the course and, probably, a senior faculty position at the university of your choice will be awarded for a solution. Our games could be viewed as ATM using a small space but up to an exponential time and returning the result of the game.
Accepted strings describe winning positions.
Weak cells as rightward, Shy leftward. The TM head is set to move upon termination to the end of the tape, so that no loser pieces are left. So, any fast algorithm to solve Linear Chess, could be used to solve any game. Since Halting Game requires exponential time, so does the Linear Chess. We know no general superlinear lower bound or subexponential upper bound for time to determine their outcome.