In this paper, we present some reduced complexity attacks on the Alternating Step Generator (ASG). The attacks are based on a quite general framework and mostly benefit from the low sampling resistance of the ASG, and of an abnormal behavior related to the distribution of the initial states of the stop/go LFSR's which produce a given segment of the output sequence. Our results compare well with previous results as they show a greater flexibility with regard to known output of the ASG, which amounts in reduced complexity. We will also give a closed form for the complexity of attacks on ASG (and SG) as presented in [13].