The Solvability of the Halting Problem for 2-State Post Machines

A Post machine is a Turing machine which cannot both write and move on the same machine step. It is shown that the halting problem for the class of 2-state Post machines is solvable. Thus, there can be no universal 2-state Post machine. This is in contrast with the result of Shannon that there exist universal 2-state Turing machines when the machines are capable of both writing and moving on the same step.