Abstract Regular Tree Model Checking

Abstract

Regular (tree) model checking (RMC) is a promising generic method for formal verification of infinite-state systems. It encodes configurations of systems as words or trees over a suitable alphabet, possibly infinite sets of configurations as finite word or tree automata, and operations of the systems being examined as finite word or tree transducers. The reachability set is then computed by a repeated application of the transducers on the automata representing the currently known set of reachable configurations. In order to facilitate termination of RMC, various acceleration schemas have been proposed. One of them is a combination of RMC with the abstract-check-refine paradigm yielding the so-called abstract regular model checking (ARMC). ARMC has originally been proposed for word automata and transducers only and thus for dealing with systems with linear (or easily linearisable) structure. In this paper, we propose a generalisation of ARMC to the case of dealing with trees which arise naturally in a lot of modelling and verification contexts. In particular, we first propose abstractions of tree automata based on collapsing their states having an equal language of trees up to some bounded height. Then, we propose an abstraction based on collapsing states having a non-empty intersection (and thus "satisfying") the same bottom-up tree "predicate" languages. Finally, we show on several examples that the methods we propose give us very encouraging verification results.

Asynchronously Communicating Visibly Pushdown Systems

“…Instead, we direct an interested reader to a survey [1]. We suspect that techniques similar to the ones developed for regular model checking, especially to those for regular tree model checking (e.g., [7]), could be applied to model check the formal model we propose.…”

Equational Abstraction Refinement for Certified Tree Regular Model Checking

“…Existing CEGAR approaches [17,15,16,11] check for spurious counter examples by performing a sequence of applications of the rewriting rules to A * R,E . To avoid this potentially costly step, we suggest to replace the merging of states by the addition of new rewriting rules that carry out information on the merging through equations.…”

“…The first abstraction-based technique for TRMC, Abstract Tree Regular Model Checking (ATRMC), was proposed by Bouajjani et al [17,15,16]. ATRMC computes sequences of automata by successive applications of the rewriting relation to the automaton representing the initial set of states.…”

Rewriting Approximations for Fast Prototyping of Static Analyzers

“…In [4], Bouajjani et al propose a verification methodology based on abstractions and tree transducer applications on tree automata languages, called Abstract Regular Tree Model Checking. This brings into play a tree transducer τ , a tree automaton A and an abstraction α.…”