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 $zapprox 14$, and (ii) a more standard Late Reionization Model (LRM) in which overlapping, induced by QSOs and normal galaxies, occurs at $zapprox 6$. 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.
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