  We consider two protocols for the measurement of the temporal correlation
functions of a dichotomic variable Q appearing in Leggett-Garg type
inequalities. The protocols measure solely whether Q has the same or different
sign at the ends of a given time interval. They are inspired, in part, by a
decoherent histories analysis of the two-time histories of Q although the
protocols are ultimately expressed in macrorealistic form independent of
quantum theory. The first type involves an ancilla coupled to the system with
two sequential CNOT gates, and the two-time histories of the system are
determined in a single final time measurement of the ancilla. It is
non-invasive for special choices of initial system states and partially
invasive for more general choices. Modified Leggett-Garg type inequalities
which accommodate the partial invasiveness are discussed. The quantum picture
of the protocol shows that for certain choices of primary system initial state
the protocol is undetectable with respect to final system state measurements,
although it is still invasive at intermediate times. This invasiveness can be
reduced with different choices of ancilla states and the protocol is then
similar in flavour to a weak measurement. The second type of protocol is based
on the fact that the behaviour of Q over a time interval can be determined from
knowledge of the dynamics together with a measurement of certain initial (or
final) data. Its quantum version corresponds to the known fact that when sets
of histories are decoherent, their probabilities may be expressed in terms of a
record projector, hence the two-time histories in which Q has the same or
different sign can be determined by a single projective measurement. The
resulting protocol resembles the decay-type protocol proposed by Huelga and
collaborators (which is non-invasive but requires a stationarity assumption).
