Abstract. The reachability analysis of recursive programs that communicate asynchronously over reliable Fifo channels calls for restrictions to ensure decidability. We extend here a model proposed by La Torre, Madhusudan and Parlato [16], based on communicating pushdown systems that can dequeue with empty stack only. Our extension adds the dual modality, which allows to dequeue with non-empty stack, and thus models interrupts for working threads. We study (possibly cyclic) network architectures under a semantic assumption on communication that ensures the decidability of reachability for finite state systems. Subsequently, we determine precisely how pushdowns can be added to this setting while preserving the decidability; in the positive case we obtain exponential time as the exact complexity bound of reachability. A second result is a generalization of the doubly exponential time algorithm of [16] for bounded context analysis to our symmetric queueing policy. We provide here a direct and simpler algorithm.
Abstract. The reachability analysis of recursive programs that communicate asynchronously over reliable Fifo channels calls for restrictions to ensure decidability. Our first result characterizes communication topologies with a decidable reachability problem restricted to eager runs (i.e., runs where messages are either received immediately after being sent, or never received). The problem is ExpTime-complete in the decidable case. The second result is a doubly exponential time algorithm for bounded context analysis in this setting, together with a matching lower bound. Both results extend and improve previous work from [21].
To make the development of efficient multi-core applications easier, libraries, such as Grand Central Dispatch, have been proposed. When using such a library, the programmer writes so-called blocks, which are chunks of codes, and dispatches them, using synchronous or asynchronous calls, to several types of waiting queues. A scheduler is then responsible for dispatching those blocks on the available cores. Blocks can synchronize via a global memory. In this paper, we propose Queue-Dispatch Asynchronous Systems as a mathematical model that faithfully formalizes the synchronization mechanisms and the behavior of the scheduler in those systems. We study in detail their relationships to classical formalisms such as pushdown systems, Petri nets, fifo systems, and counter systems. Our main technical contributions are precise worst-case complexity results for the Parikh coverability problem and the termination question for several subclasses of our model. We give an outlook on extending our model towards verifying input-parametrized fork-join behaviour with the help of abstractions.
Abstract. We present McScM, a platform for implementing and comparing verification algorithms for the class of finite-state processes exchanging messages over reliable, unbounded FIFO channels. McScM provides tools for the safety verification and controller synthesis of these infinite-state models. Our verification tool implements several modelchecking techniques: CEGAR with different abstraction-refinement methods, abstract interpretation, abstract regular model checking, and lazy abstraction. Seen as a general framework for the class of transition systems with finite control/infinite data, McScM delivers the basic infrastructure for implementing verification algorithms, and privileges to conveniently implement new ideas on a high level of abstraction. It also allows us to compare and benchmark different algorithmic approaches with the same backend.
To harness the power of multi-core and distributed platforms, and to make the development of concurrent software more accessible to software engineers, different object-oriented concurrency models such as SCOOP have been proposed. Despite the practical importance of analysing SCOOP programs, there are currently no general verification approaches that operate directly on program code without additional annotations. One reason for this is the multitude of partially conflicting semantic formalisations for SCOOP (either in theory or by-implementation). Here, we propose a simple graph transformation system (GTS) based run-time semantics for SCOOP that grasps the most common features of all known semantics of the language. This run-time model is implemented in the stateof-the-art GTS tool GROOVE, which allows us to simulate, analyse, and verify a subset of SCOOP programs with respect to deadlocks and other behavioural properties. Besides proposing the first approach to verify SCOOP programs by automatic translation to GTS, we also highlight our experiences of applying GTS (and especially GROOVE) for specifying semantics in the form of a run-time model, which should be transferable to GTS models for other concurrent languages and libraries.
Abstract. The technique of counterexample-guided abstraction refinement (Cegar) has been successfully applied in the areas of software and hardware verification. Automatic abstraction refinement is also desirable for the safety verification of complex infinite-state models. This paper investigates Cegar in the context of formal models of network protocols, in our case, the verification of fifo systems. Our main contribution is the introduction of extrapolation-based path invariants for abstraction refinement. We develop a range of algorithms that are based on this novel theoretical notion, and which are parametrized by different extrapolation operators. These are utilized as subroutines in the refinement step of our Cegar semi-algorithm that is based on recognizable partition abstractions. We give sufficient conditions for the termination of Cegar by constraining the extrapolation operator. Our empirical evaluation confirms the benefit of extrapolation-based path invariants.
We introduce ω-Petri nets (ωPN), an extension of plain Petri nets with ωlabeled input and output arcs, that is well-suited to analyse parametric concurrent systems with dynamic thread creation. Most techniques (such as the Karp and Miller tree or the Rackoff technique) that have been proposed in the setting of plain Petri nets do not apply directly to ωPN because ωPN define transition systems that have infinite branching. This motivates a thorough analysis of the computational aspects of ωPN. We show that an ωPN can be turned into an plain Petri net that allows to recover the reachability set of the ωPN, but that does not preserve termination. This yields complexity bounds for the reachability, (place) boundedness and coverability problems on ωPN. We provide a practical algorithm to compute a coverability set of the ωPN and to decide termination by adapting the classical Karp and Miller tree construction. We also adapt the Rackoff technique to ωPN, to obtain the exact complexity of the termination problem. Finally, we consider the extension of ωPN with reset and transfer arcs, and show how this extension impacts the decidability and complexity of the aforementioned problems. ReachabilityDecidable and EX- PSPACE-hard (4) Undecidable (6) Undecidable (6) Place-boundedness EXPSPACE-c (4) Boundedness Decidable (6) Coverability Decidable and Ackerman-hard (6) Problem ωPN ωOPN+T, ωOPN+R ωIPN+T, ωIPN+R Termination EXPSPACE-c (5) Undecidable (6) Decidable and Ackerman-hard (6) complexity of (plain) PN problems apply to ωPN too. However, it does not preserve termination. Thus, we study, in Section 5, as a third contribution, an extension of the self-covering path technique due to Rackoff [19]. This technique allows to provide a direct proof of EXPSPACE upper bounds for several classical decision problems, and in particular, this allows to prove EXPSPACE completeness of the termination problem.Finally, in Section 6, as a additional contribution, and to get a complete picture, we consider extensions of ωPN with reset and transfer arcs [7]. For those extensions, the decidability results for reset and transfer nets (without ω arcs) also apply to our extension with the notable exception of the termination problem that becomes, as we show here, undecidable. The summary of our results are given in Table 1.Related works ωPN are well-structured transition systems [10]. The set saturation technique [1] and so symbolic backward analysis can be applied to them while the finite tree unfolding is not applicable because of the infinite branching property of ωPN. For the same reason, ωPN are not well-structured nets [11].In [3], Bradzil et al. extends the Rackoff technique to VASS games with ω output arcs. While this extension of the Rackoff technique is technically close to ours, we cannot directly use their results to solve the termination problem of ωPN.Several works (see for instance [4,5] rely on Petri nets to model parametric systems and perform parametrised verification. However, in all these works, the dynamic creation of thread...
We introduce ω-Petri nets (ωPN), an extension of plain Petri nets with ω-labeled input and output arcs, that is well-suited to analyse parametric concurrent systems with dynamic thread creation. Most techniques (such as the Karp and Miller tree or the Rackoff technique) that have been proposed in the setting of plain Petri nets do not apply directly to ωPN because ωPN define transition systems that have infinite branching. This motivates a thorough analysis of the computational aspects of ωPN. We show that an ωPN can be turned into a plain Petri net that allows us to recover the reachability set of the ωPN, but that does not preserve termination (an ωPN terminates iff it admits no infinitely long execution). This yields complexity bounds for the reachability, boundedness, place boundedness and coverability problems on ωPN. We provide a practical algorithm to compute a coverability set of the ωPN and to decide termination by adapting the classical Karp and Miller tree construction. We also adapt the Rackoff technique to ωPN, to obtain the exact complexity of the termination problem. Finally, we consider the extension of ωPN with reset and transfer arcs, and show how this extension impacts the decidability and complexity of the aforementioned problems.
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