  We derive the analytical theory describing the process of sub-femtosecond
pulse formation from a quasi-monochromatic seeding extreme ultraviolet (XUV)
radiation, which propagates in active medium of a hydrogen-like plasma-based
X-ray laser dressed by a strong infrared laser field. We discuss the ultimate
capabilities and limitations of this process on the basis of the derived
analytical solution and extensive numerical studies for the case of Li2+
plasma-based X-ray laser with a carrier wavelength 13.5nm. We analyze the role
of plasma dispersion and find the optimal conditions for the formation of
attosecond pulses with the highest contrast. Under the optimal conditions, the
influence of amplified spontaneous emission from the active medium is
negligible. The peak intensity of the produced XUV pulses can exceed
10^10-10^11 W/cm^2, while the duration of pulses varies in the range of 400-600
as.
