 Accelerating Turing machines (ATMs) are exactly like standard Turing machines except that their speed of operation accelerates as the computation proceeds (Stewart 1991; Copeland 1998a,b, 2002a; Copeland and Shagrir 2011): an ATM performs the second operation called for by its program in half the time taken to perform the first, the third in half the time taken to perform the second, and so on.