  We propose a novel algorithm for automata-based LTL model checking that
interleaves the construction of the generalized B\"{u}chi automaton for the
negation of the formula and the emptiness check. Our algorithm first converts
the LTL formula into a linear weak alternating automaton; configurations of the
alternating automaton correspond to the locations of a generalized B\"{u}chi
automaton, and a variant of Tarjan's algorithm is used to decide the existence
of an accepting run of the product of the transition system and the automaton.
Because we avoid an explicit construction of the B\"{u}chi automaton, our
approach can yield significant improvements in runtime and memory, for large
LTL formulas. The algorithm has been implemented within the SPIN model checker,
and we present experimental results for some benchmark examples.
