Laurent Van Begin

Towards the Automated Verification of Multithreaded Java Programs

In this paper we investigate the possible application of parameterized verification techniques to synchronization skeletons of multithreaded Java programs. As conceptual contribution, we identify a class of infinite-state abstract models, called Multi-Transfer Nets (MTNs), that preserve the main features of the semantics of concurrent Java. We achieve this goal by exploiting an interesting connection with the Broadcast Protocols of [7], and by introducing the notion of asynchronous rendez-vous. As technical contribution, we extend the symbolic verification techniques of [6] based on Covering Sharing Trees and structural invariants to MTNs. As practical contribution, we report on experimental results for verification of examples of multithreaded Java programs.

A complete abstract interpretation framework for coverability properties of WSTS

We present an abstract interpretation based approach to solve the coverability problem of well-structured transition systems. Our approach distinguishes from other attempts in that (1) we solve this problem for the whole class of well-structured transition systems using a forward algorithm. So, our algorithm has to deal with possibly infinite downward closed sets. (2) Whereas other approaches have a non generic representation for downward closed sets of states, which turns out to be hard to devise in practice, we introduce a generic representation requiring no additional effort of implementation.

Covering sharing trees: a compact data structure for parameterized verification

The control state reachability problem is decidable for well-structured infinite-state systems like (Lossy) Petri Nets, Vector Addition Systems, and broadcast protocols. An abstract algorithm that solves the problem is the backward reachability algorithm of [1, 21 ]. The algorithm computes the closure of the predecessor operator with respect to a given upward-closed set of target states. When applied to this class of verification problems, symbolic model checkers based on constraints like [7, 26 ] suffer from the state explosion problem.In order to tackle this problem, in [13] we introduced a new data structure, called covering sharing trees, to represent in a compact way collections of infinite sets of system configurations. In this paper, we will study the theoretical complexity of the operations over covering sharing trees needed in symbolic model checking. We will also discuss several optimizations that can be used when dealing with Petri Nets. Among them, in [14] we introduced a new heuristic rule based on structural properties of Petri Nets that can be used to efficiently prune the search during symbolic backward exploration. The combination of these techniques allowed us to turn the abstract algorithm of [1, 21 ] into a practical method. We have evaluated the method on several finite-state and infinite-state examples taken from the literature [2, 18 , 20 , 30 ]. In this paper, we will compare the results we obtained in our experiments with those obtained using other finite and infinite-state verification tools.

Attacking Symbolic State Explosion

We propose a new symbolic model checking algorithm for parameterized concurrent systems modeled as (Lossy) Petri Nets, and (Lossy) Vector Addition Systems, based on the following ingredients: a rich assertional language based on the graph-based symbolic representation of upward-closed sets introduced in [DR00], the combination of the backward reachability algorithm of [ACJT96] lifted to the symbolic setting with a new heuristic rule based on structural properties of Petri Nets. We evaluate the method on several Petri Nets and parameterized systems taken from the literature [ABC+95, EM00, Fin93, MC99], and we compare the results with other finite and infinite-state verification tools.

Monotonic extensions of petri nets: Forward and backward search revisited

In this paper, we revisit the forward and backward approaches to the verification of extensions of infinite state Petri Nets. As contributions, we propose an efficient data structure to represent infinite downward closed sets of markings and to compute symbolically the minimal coverability set of Petri Nets, we identify a subclass of Transfer Nets for which the forward approach generalizes and we propose a general strategy to use both the forward and the backward approach for the efficient verification of general Transfer Nets.

On the efficient computation of the minimal coverability set of petri nets

The minimal coverability set (MCS) of a Petri net is a finite representation of the downward-closure of its reachable markings. The minimal coverability set allows to decide several important problems like coverability, semi-liveness, place boundedness, etc. The classical algorithm to compute the MCS constructs the Karp&Miller (KM) tree [10]. Unfortunately the KM tree is often huge, even for small nets. An improvement of this KM algorithm is the Minimal Coverability Tree (MCT) algorithm [3], which has been introduced nearly 20 years ago, and implemented since then in several tools such as Pep [9]. Unfortunately, we show in this paper that the MCT is flawed: it might compute an under-approximation of the reachable markings. We propose a new solution for the efficient computation of the MCS of Petri nets. Our algorithm is based on new ideas, and the experimental results show that it behaves much better in practice than the KM algorithm.

Well-structured languages

This paper introduces the notion of well-structured language. A well-structured language can be defined by a labelled well-structured transition system, equipped with an upward-closed set of accepting states. That peculiar class of transition systems has been extensively studied in the field of computer-aided verification, where it has direct an important applications. Petri nets, and their monotonic extensions (like Petri nets with non-blocking arcs or Petri nets with transfer arcs), for instance, are special subclasses of well-structured transition systems. We show that the class of well-structured languages enjoy several important closure properties. We propose several pumping lemmata that are applicable respectively to the whole class of well-structured languages and to the classes of languages recognized by Petri nets or Petri nets with non-blocking arcs. These pumping lemmata allow us to characterize the limits in the expressiveness of these classes of language. Furthermore, we exploit the pumping lemmata to strictly separate the expressive power of Petri nets, Petri nets with non-blocking arcs and Petri nets with transfer arcs.

A classification of the expressive power of well-structured transition systems

We compare the expressive power of a class of well-structured transition systems that includes relational automata (extensions of), Petri nets, lossy channel systems, constrained multiset rewriting systems, and data nets. For each one of these models we study the class of languages generated by labeled transition systems describing their semantics. We consider here two types of accepting conditions: coverability and reachability of a fixed a priori configuration. In both cases we obtain a strict hierarchy in which constrained multiset rewriting systems is the most expressive model.

On the efficient computation of the minimal coverability set for Petri nets

The minimal coverability set (MCS) of a Petri net is a finite representation of the downward-closure of its reachable markings. The minimal coverability set allows to decide several important problems like coverability, semi-liveness, place boundedness, etc. The classical algorithm to compute the MCS constructs the Karp&Miller tree [8]. Unfortunately the K&M tree is often huge, even for small nets. An improvement of this K&M algorithm is the Minimal Coverability Tree (MCT) algorithm [1], which has been introduced 15 years ago, and implemented since then in several tools such as Pep [7]. Unfortunately, we show in this paper that the MCT is flawed: it might compute an under-approximation of the reachable markings. We propose a new solution for the efficient computation of the MCS of Petri nets. Our experimental results show that this new algorithm behaves much better in practice than the K&M algorithm.

A Language-Based Comparison of Extensions of Petri Nets with and without Whole-Place Operations

We use language theory to study the relative expressiveness of infinite-state models laying in between finite automata and Turing machines. We focus here our attention on well structured transition systems that extend Petri nets. For these models, we study the impact of whole-place operations like transfers and resets on nets with indistinguishable tokens and with tokens that carry data over an infinite domain. Our measure of expressiveness is defined in terms of the class of languages recognized by a given model using coverability of a configuration as accepting condition.