Truly On-the-Fly LTL Model Checking

Abstract

Abstract. We propose a novel algorithm for automata-based LTL model checking that interleaves the construction of the generalized Büchi 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 Büchi 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 Büchi 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.

On-the-Fly Emptiness Checks for Generalized Büchi Automata

“…We could not reproduce the important contrast they show between these two algorithms (neither could Hammer et al [12]). For example, the 94 formulae (and their negation) from the literature have been checked against 15 random graphs with a transition probability of 0.001.…”

“…If the union of all the acceptance conditions occurring in a non-trivial SCC is F , and that SCC is accessible from q 0 , then one can assert the existence of such an accepting run. This is the essence of the algorithms of Couvreur [3], Geldenhuys and Valmari [8,9], and Hammer et al [12].…”

“…Hammer et al [12]'s algorithm is presented as an emptiness check for Linear Weak Alternating Automata (LWAA). However their algorithm translates an LWAA into a generalized Büchi automata on-the-fly during the emptiness check.…”

Fair Model Checking with Process Counter Abstraction

“…The sound but incomplete approaches include methods based on synthesis of invisible invariant (e.g., [10]); methods based on network invariant (e.g., [21]) that relies on the effectiveness of a generated invariant and the invariant refinement techniques; regular model checking [19] that requires acceleration techniques. Verification of liveness properties under fairness constraints have been studied in [15,17,20]. These works are based on SCC-related algorithms and decide the existence of an accepting run of the product of the transition system and Büchi automata, Streett automata or linear weak alternating automaton.…”

GOAL Extended: Towards a Research Tool for Omega Automata and Temporal Logic

“…Another effort will be to include even more translation algorithms, in particular those that utilize intermediary automata with acceptance conditions on transitions such as [17] and those that do simplification while constructing automata on-the-fly [7]. The fact that Safra's and Piterman's algorithms in average work better than complementation via WAPA and complementation via WAA is also worthy of further investigation.…”