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We apply the symbolic analysis principle to pushdown systems. We represent (possibly infinite) sets of configurations of such systems by means of finite-state automata. In order to reason in a uniform way about analysis problems involving both existential and universal path quantification (such as model-checking for branching-time logics), we consider the more general class of alternating pushdown systems and use alternating finite-state automata as a representation structure for sets of their configurations. We give a simple and natural procedure to compute sets of predecessors using this representation structure. We incorporate this procedure into the automata-theoretic approach to model-checking to define new model-checking algorithms for pushdown systems against both linear and branching-time properties. From these results we derive upper bounds for several model-checking problems as well as …