  We propose a lazy decision procedure for the logic WSkS. It builds a
term-based symbolic representation of the state space of the tree automaton
(TA) constructed by the classical WSkS decision procedure. The classical
decision procedure transforms the symbolic representation into a TA via a
bottom-up traversal and then tests its language non-emptiness, which
corresponds to satisfiability of the formula. On the other hand, we start
evaluating the representation from the top, construct the state space on the
fly, and utilize opportunities to prune away parts of the state space
irrelevant to the language emptiness test. In order to do so, we needed to
extend the notion of language terms (denoting language derivatives) used in our
previous procedure for the linear fragment of the logic (the so-called WS1S)
into automata terms. We implemented our decision procedure and identified
classes of formulae on which our prototype implementation is significantly
faster than the classical procedure implemented in the Mona tool.
