i ; and H T halts on a nonblank tape, scanning an appropriate field (which however does not necessarily carry the symbol "1") if and only if the Turing machine represented by a does halt when given the starting state and input represented by i . In this case, the final state in which H T halted (contents of the tape, and field being scanned) shall be equal to some particular intermediate state which the Turing machine represented by a attains when given the starting state and input represented by i ; or, if all those intermediate states (including the starting state represented by i ) leave the tape blank, then the final state in which H T halted shall be scanning a "1" on an otherwise blank tape. While its existence has not been refuted (essentially: because there's no Turing machine which would halt only if started on a blank tape), such a Turing machine H T would solve the halting problem only partially either (because it doesn't necessarily scan the symbol "1" in the final state, if the Turing machine represented by a does halt when given the starting state and input represented by i , as explicit statements of the halting problem for Turing machines may require). 1920–1921: Emil Post explores the halting problem for tag systems, regarding it as a candidate for unsolvability. ( Absolutely unsolvable problems and relatively undecidable propositions – account of an anticipation , in Davis, 1965, pp. 340–433.) Its unsolvability was not