Efficient Decision Procedures for Model Checking of Linear Time Logic Properties

Abstract

We propose an algorithm for LTL model checking based on the classification of the automata and on guided symbolic search. Like most current methods for LTL model checking, our algorithm starts with a tableau construction and uses a model checker for CTL with fairness constraints to prove the existence of fair paths. However, we classify the tableaux according to their structure, and use efficient decision procedures for each class. Guided search applies hints to constrain the transition relation during fixpoint computations. Each fixpoint is thus translated into a sequence of fixpoints that are often much easier to compute than the original one. Our preliminary experimental results suggest that the new algorithm for LTL is quite efficient. In fact, for properties that can be expressed in both CTL and LTL, the algorithm is competitive with the CTL model checking algorithm.

Relating Hierarchy of Temporal Properties to Model Checking

“…Schneider [19] is concerned with a translation of persistence properties into weak automata. Bloem and Somenzi study heuristics for the translation of a formula into weak (terminal) automaton [21] and suggest specialised algorithms for the non-emptiness problem [1]. Our work covers all types of properties and brings out the correspondence between the type and the complexity of non-emptiness check.…”

“…To classify nondeterministic Büchi automata we adopt the criteria proposed by Bloem, Ravi, and Somenzi [1]. They differentiate general, weak, and terminal automata according to the following restrictions posed on their transition functions: …”

“…The explicit algorithm has to use only a single DFS [8] in this case. With the symbolic representation single fixpoint computation [1] with a linear number of steps is sufficient.…”

“…Edelkamp, Lafuente, and Leue [8] extended the explicit model checker SPIN by a non-emptiness algorithm which to a certain extent takes the type of an automaton into consideration. Bloem, Ravi, and Somenzi [1] performed experiments with symbolic algorithms and in [2] experiments with distributed algorithms are presented.…”

“…The complexity of the non-emptiness check depends on the type of the automaton. Bloem, Ravi, and Somenzi [1] have studied two specialised types of automata, called weak and terminal, for which the non-emptiness check can be performed more efficiently than in the general case.…”