A genral Turing model with one tape to define sublinear space (L,NL,..)
Normally to define sub-linear space complexity we need special Turing models with many tapes, at least two: a read-only tape and a work tape; or often three: with an additional output tape. (We do this because the reading of the input would cost us linear space.)
I'm looking for a general Turing model with just one tape and one consistent definition for space and for complexity that works in all the cases, inclusively the sub-linear case of L (Logspace), NL (NLogspace).. and the more famous P, NP, PSPACE etc.
For this purpose obviously we must change the space definition - but how best?
EDIT: For example: if we just count the new written cells in a one-tape machine would this solve the problem?