Abstraction-Guided Model Checking Using Symbolic IDA* and Heuristic Synthesis

Abstract

A heuristic-based symbolic model checking algorithm, BDD-IDA * that efficiently falsifies invariant properties of a system is presented. As in bounded model checking, the algorithm uses an iterative deepening search strategy. However, in our case, the search strategy is guided by a heuristic that is computed from an abstract model, which is derived from the concrete model by a synthesis technique. Synthesis involves eliminating so-called weak variables from the concrete specification, where the weak variables are identified by a datadependency analysis. Unique to this work is the use of the depth-first IDA * search algorithm in a BDD setting, and the automatic synthesis of the heuristic. The performance of the approach on a large number of small examples is compared with standard BDD-based approaches. Experiments on a variety of real-world models from different domains are also conducted. The approach reveals a consistent improvement on all models, and in some cases a speed-up of 2 orders of magnitude is obtained.

Transition-Based Directed Model Checking

“…The distance estimation function is read off the overall merged automaton. Moreover, several distance estimation functions based on pattern databases have been proposed [9,13,17,18]. A pattern database heuristic function abstracts a problem by ignoring some of the relevant symbols, e. g., some of the state variables.…”

“…Earlier work on directed model checking was mainly focused on the first point, i. e., in defining abstractions that lead to distance estimation functions d # to guide the state space traversal efficiently towards an error state [3,4,5,9,12,13,17,18]. Considering the second point, there are two predominantly used algorithms of directed model checking, namely A * and greedy search (cf.…”

Fast Directed Model Checking Via Russian Doll Abstraction

“…Groce and Visser [3] define heuristics inspired from the area of testing, with the idea to prefer covering yet unexplored branches in the program. Qian and Nymeyer [4,8] ignore some of the state variables to define heuristics which are then used in a pattern database approach (see below). Kupferschmid et al [5] adapt a heuristic method from the area of AI Planning, based on a notion of "monotonicity" where it is assumed that a state variable accumulates, rather than changes, its values.…”

“…In our work, we extend and improve upon a new kind of strategy to choose a PDB abstraction. The strategy is particularly well suited for model checking; a first version of it was explored by Qian and Nymeyer [8]. It is based on what we call a Russian Doll principle.…”

“…The basic idea is to do some form of abstract cone-of-influence [11] computation, and ignore those symbols that do not appear in the cone-of-influence. Qian and Nymeyer [8] use a simple syntactic backward chaining process that iteratively collects variable names and requires the user to specify a threshold on the maximal considered "distance" -number of iterations -of the kept variables from the safety property. In our work, we use a more sophisticated procedure based on the abstraction techniques of Kupferschmid et al [5].…”