César Rodríguez

Efficient unfolding of contextual Petri nets

A contextual net is a Petri net extended with read arcs, which allows transitions to check for tokens without consuming them. Contextual nets allow for better modelling of concurrent read access than Petri nets, and their unfoldings can be exponentially more compact than those of a corresponding Petri net. A constructive but abstract procedure for generating those unfoldings was proposed in previous work. However, it remained unclear whether the approach was useful in practice and which data structures and algorithms would be appropriate to implement it. Here, we address this question. We provide two concrete methods for computing contextual unfoldings, with a view to efficiency. We report on experiments carried out on a number of benchmarks. These show that not only are contextual unfoldings more compact than Petri net unfoldings, but they can be computed with the same or better efficiency, in particular with respect to alternative approaches based on encodings of contextual nets into Petri nets.

Unfolding-based Partial Order Reduction

Partial order reduction (POR) and net unfoldings are two alternative methods to tackle state-space explosion caused by concurrency. In this paper, we propose the combination of both approaches in an effort to combine their strengths. We first define, for an abstract execution model, unfolding semantics parameterized over an arbitrary independence relation. Based on it, our main contribution is a novel stateless POR algorithm that explores at most one execution per Mazurkiewicz trace, and in general, can explore exponentially fewer, thus achieving a form of super-optimality. Furthermore, our unfolding-based POR copes with non-terminating executions and incorporates state-caching. Over benchmarks with busy-waits, among others, our experiments show a dramatic reduction in the number of executions when compared to a state-of-the-art DPOR.

Verification of petri nets with read arcs

Recent work studied the unfolding construction for contextual nets, i.e. nets with read arcs. Such unfoldings are more concise and can usually be constructed more efficiently than for Petri nets. However, concrete verification algorithms exploiting these advantages were lacking so far. We address this question and propose SAT-based verification algorithms for deadlock and reachability of contextual nets. Moreover, we study optimizations of the SAT encoding and report on experiments.

Cunf: A Tool for Unfolding and Verifying Petri Nets with Read arcs

Cunf is a tool for building and analyzing unfoldings of Petri nets with read arcs. An unfolding represents the behaviour of a net by a partial order, effectively coping with the state-explosion problem stemming from the interleaving of concurrent actions. C-net unfoldings can be up to exponentially smaller than Petri net unfoldings, and recent work proposed algorithms for their construction and verification. Cunf is the first implementation of these techniques, it has been carefully engineered and optimized to ensure that the theoretical gains are put into practice.

Reveal Your Faults: It's Only Fair!

We present a methodology for fault diagnosis in concurrent, partially observable systems with additional fairness constraints. In this weak diagnosis, one asks whether a concurrent chronicle of observed events allows to determine that a non-observable fault will inevitably occur, sooner or later, on any maximal system run compatible with the observation. The approach builds on strengths and techniques of unfoldings of safe Petri nets, striving to compute a compact prefix of the unfolding that carries sufficient information for the diagnosis algorithm. Our work extends and generalizes the unfolding-based diagnosis approaches by Benveniste et al. [1] as well as Esparza and Kern [2]. Both of these focused mostly on the use of sequential observations, in particular did not exploit the capacity of unfoldings to reveal inevitable occurrences of concurrent or future events studied by Balaguer et al. [3]. Our diagnosis method captures such indirect, revealed dependencies. We develop theoretical foundations and an algorithmic solution to the diagnosis problem, and present a SAT solving method for practical diagnosis with our approach.

Contextual merged processes

We integrate two compact data structures for representing state spaces of Petri nets: merged processes and contextual prefixes. The resulting data structure, called contextual merged processes (CMP), combines the advantages of the original ones and copes with several important sources of state space explosion: concurrency, sequences of choices, and concurrent read accesses to shared resources. In particular, we demonstrate on a number of benchmarks that CMPs are more compact than either of the original data structures. Moreover, we sketch a polynomial (in the CMP size) encoding into SAT of the model-checking problem for reachability properties.

Efficient contextual unfolding

A contextual net is a Petri net extended with read arcs, which allow transitions to check for tokens without consuming them. Contextual nets allow for better modelling of concurrent read access than Petri nets, and their unfoldings can be exponentially more compact than those of a corresponding Petri net. A constructive but abstract procedure for generating those unfoldings was proposed in earlier work; however, no concrete implementation existed. Here, we close this gap providing two concrete methods for computing contextual unfoldings, with a view to efficiency. We report on experiments carried out on a number of benchmarks. These show that not only are contextual unfoldings more compact than Petri net unfoldings, but they can be computed with the same or better efficiency, in particular with respect to the place-replication encoding of contextual nets into Petri nets.

An Improved Construction of Petri Net Unfoldings

Petri nets are a well-known model language for concurrent systems. The unfolding of a Petri net is an acyclic net bisimilar to the original one. Because it is acyclic, it admits simpler decision problems though it is in general larger than the net. In this paper, we revisit the problem of efficiently constructing an unfolding. We propose a new method that avoids computing the concurrency relation and therefore uses less memory than some other methods but still represents a good time-space tradeoff. We implemented the approach and report on experiments.

Construction and SAT-based verification of contextual unfoldings

Unfoldings succinctly represent the set of reachable markings of a Petri net. Here, we shall consider the case of contextual nets, which extend Petri nets with read arcs, and which are more suitable to represent the case of concurrent read access. We discuss the problem of (efficiently) constructing unfoldings of such nets. On the basis of these unfoldings, various verification problems can be encoded as satisfiability problems in propositional logic.