  Attosecond x-ray pulses play a crucial role in the study of ultrafast
phenomena occurring within inner and valence electrons. To achieve attosecond
time-resolution studies and gain control over electronic wavefunctions, it is
crucial to develop techniques capable of generating and synchronizing two-color
x-ray pulses at the attosecond scale. In this paper, we present a novel
approach for generating attosecond pulse pairs using a dual chirp-taper
free-electron laser with bunching inheritance. An electron beam with a
sinusoidal energy chirp, introduced by the external seed laser, passes through
the main undulator and afterburner, both with tapers. Two-color x-ray pulses
are generated from the main undulator and afterburner, respectively, with
temporal separations of hundreds of attoseconds to several femtoseconds and
energy differences of tens of electron volts. Notably, the afterburner is much
shorter than the main undulator due to bunching inheritance, which reduces the
distance between two source points and alleviates the beamline focusing
requirements of the two-color pulses. A comprehensive stability analysis is
conducted in this paper, considering the individual effects of shot noise from
self-amplified spontaneous emission and carrier-envelope phase jitter of the
few-cycle laser. The results show that the radiation from the afterburner
exhibits excellent stability in the proposed scheme, which is beneficial for
x-ray pump-probe experiments. The proposed scheme opens up new possibilities
for attosecond science enabled by x-ray attosecond pump-probe techniques and
coherent control of ultrafast electronic wave packets in quantum systems.
