In this paper we present two new practical and pragmatic algorithms for solving the two key on-the-fly model-checking problems for linear temporal logic: on demand construction of an automaton for a temporal logic formula; and on-the-fly checking for whether the automata resulting from the product of the program and the property is empty.

Abstract. Emptiness check is a key operation in the automata-theoretic approach to LTL verification. However, it is usually done on Büchi automata with a single acceptance condition. We review existing on-the-fly emptiness-check algorithms for generalized Büchi automata (i.e., with multiple acceptance conditions) and show how they compete favorably with emptiness-checks for degeneralized automata, especially in presence of weak fairness assumptions. We also introduce a new emptiness-check algorithm, some heuristics to improve existing checks, and propose algorithms to compute accepting runs in the case of multiple acceptance conditions.