On the Difference Between Turing Machine Time and Random-Access Machine Time

We introduce a model of computation called the Block Move (BM) model. The BM extends the Block Transfer (BT) model of Aggarwal, Chandra, and Snir 1], who studied time complexity under various memory access cost functions ranging from 1 (a) := a to log (a) := dlog 2 ae. We show that up to factors of log t in the total running time t, BMs under 1 are equivalent to multitape Turing machines, and BMs under log are equivalent to log-cost RAMs. We also prove that for any well-behaved the BM classes DTIMEEt(n)] form a tight deterministic time hierarchy. Whether there is any hierarchy at all when rather than t varies is tied to long-standing open problems of determinism vs. nondeterminism.