  We use a semi-analytical approach to simulate absorption spectra of QSOs at
high redshifts with the aim of constraining the cosmic reionization history. We
consider two physically motivated and detailed reionization histories: (i) an
Early Reionization Model (ERM) in which the intergalactic medium is reionized
by PopIII stars at $z\approx 14$, and (ii) a more standard Late Reionization
Model (LRM) in which overlapping, induced by QSOs and normal galaxies, occurs
at $z\approx 6$. From the analysis of current Ly$\alpha$ forest data at $z <
6$, we conclude that it is impossible to disentangle the two scenarios, which
fit equally well the observed Gunn-Peterson optical depth, flux probability
distribution function and dark gap width distribution. At $z>6$, however, clear
differences start to emerge which are best quantified by the dark gap and peak
width distributions. We find that 35 (zero) per cent of the lines of sight
within $5.7< z <6.3$ show dark gaps widths $>50$ Angstrom in the rest frame of
the QSO if reionization is not (is) complete at $z \gtrsim 6$. Similarly, the
ERM predicts peaks of width $\sim 1$ Angstrom in 40 per cent of the lines of
sight in the redshift range $6.0-6.6$; in the same range, LRM predicts no peaks
of width $>0.8$ Angstrom. We conclude that the dark gap and peak width
statistics represent superb probes of cosmic reionization if about ten QSOs can
be found at $z > 6$. We finally discuss strengths and limitations of our
method.
