Combining Explicit and Symbolic LTL Model Checking Using Generalized Testing Automata

Abstract

In automata-theoretic model checking, there are mainly two approaches: explicit and symbolic. In the explicit approach [1], the state-space is constructed explicitly and lazily during exploration (i.e., on-the-fly). The symbolic approach [2] tries to overcome the state-space explosion obstacle by symbolically encoding the state-space in a concise way using decision diagrams. However, this symbolic construction is not performed on-the-fly as in the explicit approach. In order to take advantage of the best of both worlds, hybrid approaches [3, 4, 5] are proposed as combinations of explicit and symbolic approaches. A hybrid approach is usually based on an on-the-fly construction of an explicit graph of symbolic nodes, where each symbolic node encodes a subset of states by means of binary decision diagrams. An alternative to the standard Büchi automaton, called Testing automaton [6] has never been used before for hybrid model checking. In addition, in previous work [7, 8], we have shown that Generalized Testing Automata (TGTA) can outperform the Büchi automata for explicit and symbolic model checking of stutter-invariant LTL properties. In this work, we investigate the use of these TGTA to improve hybrid model checking. We show how traditional hybrid approaches based on Generalized Büchi Automata (TGBA) can be adapted to obtain TGTA-based hybrid approaches. Then, each original approach is experimentally compared against its TGTA variant. The results show that these new variants are statistically more efficient.